Skocz do pozycji: 1.

Tytuł:

A degree theory for almost continuous functions

Autorzy:

DeKleine, H.
Girolo, Jack

Powiązania:

https://bibliotekanauki.pl/articles/1364155.pdf

Data publikacji:

1978

Wydawca:

Polska Akademia Nauk. Instytut Matematyczny PAN

Źródło:

Fundamenta Mathematicae; 1978, 101, 1; 39-52
0016-2736

Pojawia się w:

Fundamenta Mathematicae

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 2.

Tytuł:

On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)

Autorzy:

Staněk, Svatoslav

Powiązania:

https://bibliotekanauki.pl/articles/1311664.pdf

Data publikacji:

1994

Wydawca:

Polska Akademia Nauk. Instytut Matematyczny PAN

Tematy:

Leray-Schauder degree theory
functional boundary conditions
boundary value problem depending on the parameter

Opis:

The Leray-Schauder degree theory is used to obtain sufficient conditions for the existence and uniqueness of solutions for the boundary value problem x'' = f(t,x,x',x'',λ), α(x) = 0, β(x̅) = 0, γ(x̿)=0, depending on the parameter λ. Here α, β, γ are linear bounded functionals defined on the Banach space of C⁰-functions on [0,1] and x̅(t) = x(0) - x(t), x̿(t)=x(1)-x(t).

Źródło:

Annales Polonici Mathematici; 1994, 59, 3; 225-237
0066-2216

Pojawia się w:

Annales Polonici Mathematici

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 3.

Tytuł:

Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions

Autorzy:

R., D.
Wang, Haiyan

Powiązania:

https://bibliotekanauki.pl/articles/1294312.pdf

Data publikacji:

1998

Wydawca:

Polska Akademia Nauk. Instytut Matematyczny PAN

Tematy:

nonlinear boundary value problems
multiplicity of positive solutions
upper and lower solutions
degree theory

Opis:

We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.

Źródło:

Annales Polonici Mathematici; 1998, 69, 2; 155-165
0066-2216

Pojawia się w:

Annales Polonici Mathematici

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 4.

Tytuł:

Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

Autorzy:

Agarwal, R.
O'Regan, D.
Sahu, D.

Powiązania:

https://bibliotekanauki.pl/articles/729475.pdf

Data publikacji:

2007

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

multivalued maps
Fréchet space
degree and index theory
projective limit

Opis:

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

Źródło:

Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 399-409
1509-9407

Pojawia się w:

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 5.

Tytuł:

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Autorzy:

Kamenskii, Mikhail
Obukhovskii, Valeri
Yao, Jen-Chih

Powiązania:

https://bibliotekanauki.pl/articles/729536.pdf

Data publikacji:

2013

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

operator differential inclusion
neutral type
periodic solution
fixed point
multivalued map
condensing map
topological degree
averaging method
control system
distributed control

Opis:

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.

Źródło:

Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 193-204
1509-9407

Pojawia się w:

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 6.

Tytuł:

Key moments of the mutual influence of the Polish and Soviet schools of nonlinear functional analysis in the 1920s--1950s

Autorzy:

Bogatov, Egor Mikhailovich

Powiązania:

https://bibliotekanauki.pl/articles/749784.pdf

Data publikacji:

2017

Wydawca:

Polskie Towarzystwo Matematyczne

Tematy:

Polish school of functional analysis, Soviet school of functional analysis, fixed point theorem, Orlicz space, nonlinear integral equations, mapping degree, convex sets, retracts theory
Polska szkoła analizy funkcjonalnej, radziecka szkoła analizy funkcjonalnej, twierdzenie o punkcie stałym, przestrzeń Orlicza, nieliniowe równanie całkowe, stopień odwzorowania, zbiory wypukłe, teoria retraktów

Opis:

Artykuł zawiera kluczowe aspekty historii rozwoju metod jakościowych nieliniowej analizy funkcjonalnej (twierdzenia o punkcie stałym, teoria stopnia odwzorowania, teoria przestrzeni Orlicza), w~ramach których najbardziej uwidoczniły się wzajemne oddziaływania polsko-radzieckie. Do połowy XX wieku w dziedzinach tych  dokonał się  postęp za sprawą  przedstawicieli lwowskiej szkoły matematycznej, warszawskiej szkoły matematycznej, moskiewskiej szkoły matematycznej  i odeskiej szkoły matematycznej. Analiza ich rezultatów stanowi główną część niniejszej pracy. Szczególną uwagę zwracamy na badania matematyka radzieckiego M. A. Krasnosel'skiego, który korzystał z wyników J. Schaudera i K. Borsuka oraz z przestrzeni Orlicza przy rozwiązywaniu szerokiej klasy problemów z jakościowej teorii nieliniowych równań całkowych.
The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within the framework of which Polish-Soviet interaction was most clearly manifested. In the period up to the mid-twentieth century these areas were advanced by the representatives of Lvov Mathematical School, Warsaw Mathematical School, Moscow Mathematical School and Odessa Mathematical School. Examination of their results is a significant part of this work. Much attention is paid to the investigations of the Soviet mathematician M.A. Krasnosel'skii, who used the achievements of J. Schauder and K. Borsuk as well as Orlicz spaces for solving a wide class of problems in qualitative theory of nonlinear integral equations. 

Źródło:

Antiquitates Mathematicae; 2017, 11
1898-5203
2353-8813

Pojawia się w:

Antiquitates Mathematicae

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 7.

Tytuł:

An application of graph theory to linguistic complexity

Autorzy:

Piperski, Alexander

Powiązania:

https://bibliotekanauki.pl/articles/1151871.pdf

Data publikacji:

2014

Wydawca:

Uniwersytet im. Adama Mickiewicza w Poznaniu

Tematy:

linguistic complexity
morphology
graph theory
average vertex degree

Opis:

This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.

Źródło:

Yearbook of the Poznań Linguistic Meeting; 2014, 1, 1
2449-7525

Pojawia się w:

Yearbook of the Poznań Linguistic Meeting

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 8.

Tytuł:

An application of graph theory to linguistic complexity

Autorzy:

Piperski, Alexander

Powiązania:

https://bibliotekanauki.pl/articles/2135360.pdf

Data publikacji:

2014-11-19

Wydawca:

Uniwersytet im. Adama Mickiewicza w Poznaniu

Tematy:

linguistic complexity
morphology
graph theory
average vertex degree

Opis:

This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.

Źródło:

Yearbook of the Poznań Linguistic Meeting; 2014, 1, 1; 89-102
2449-7525

Pojawia się w:

Yearbook of the Poznań Linguistic Meeting

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 9.

Tytuł:

Equivariant Nielsen theory

Autorzy:

Wong, Peter

Powiązania:

https://bibliotekanauki.pl/articles/1341580.pdf

Data publikacji:

1999

Wydawca:

Polska Akademia Nauk. Instytut Matematyczny PAN

Tematy:

Nielsen number
fixed point theory
homogeneous space
equivariant maps
degree
root theory

Źródło:

Banach Center Publications; 1999, 49, 1; 253-258
0137-6934

Pojawia się w:

Banach Center Publications

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 10.

Tytuł:

Acyclic 6-Colouring of Graphs with Maximum Degree 5 and Small Maximum Average Degree

Autorzy:

Fiedorowicz, Anna

Powiązania:

https://bibliotekanauki.pl/articles/30146851.pdf

Data publikacji:

2013-03-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

acyclic colouring
bounded degree graph
maximum average degree

Opis:

A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . ., k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, every cycle in G has at least three distinct colours. Acyclic colourings were introduced by Gr¨unbaum in 1973, and since then have been widely studied. In particular, the problem of acyclic colourings of graphs with bounded maximum degree has been investigated. In 2011, Kostochka and Stocker showed that any graph with maximum degree 5 can be acyclically coloured with at most 7 colours. The question, whether this bound is achieved, remains open. In this note we prove that any graph with maximum degree 5 and maximum average degree at most 4 admits an acyclic 6-colouring. We also provide examples of graphs with these properties.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 1; 91-99
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 11.

Tytuł:

The Degree-Diameter Problem for Outerplanar Graphs

Autorzy:

Dankelmann, Peter
Jonck, Elizabeth
Vetrík, Tomáš

Powiązania:

https://bibliotekanauki.pl/articles/31341627.pdf

Data publikacji:

2017-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

outerplanar
diameter
degree
degree-diameter problem
distance
separator theorem

Opis:

For positive integers $ \Delta $ and $ D $ we define $ n_{ \Delta, D } $ to be the largest number of vertices in an outerplanar graph of given maximum degree $ \Delta $ and diameter $D$. We prove that $n_{ \Delta , D} = \Delta^{D/2} + O ( \Delta^{ D/2 -1 } ) $ if $D$ is even, and $ n_{ \Delta, D} = 3 \Delta^\frac{D−1}{2} + O (\Delta^{ \frac{D−1}{2}−1 } ) $ if $D$ is odd. We then extend our result to maximal outerplanar graphs by showing that the maximum number of vertices in a maximal outerplanar graph of maximum degree $ \Delta $ and diameter $D$ asymptotically equals$ n_{ \Delta , D }.

Źródło:

Discussiones Mathematicae Graph Theory; 2017, 37, 3; 823-834
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 12.

Tytuł:

Degree of convergence of some sequences in the conformal mapping theory

Autorzy:

Siciak, J.

Powiązania:

https://bibliotekanauki.pl/articles/725787.pdf

Data publikacji:

1967

Wydawca:

Polska Akademia Nauk. Instytut Matematyczny PAN

Źródło:

Colloquium Mathematicum; 1967, 16, 1; 49-59
0010-1354

Pojawia się w:

Colloquium Mathematicum

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 13.

Tytuł:

Degree sequences of monocore graphs

Autorzy:

Bickle, Allan

Powiązania:

https://bibliotekanauki.pl/articles/30148681.pdf

Data publikacji:

2014-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

monocore graph
degeneracy
degree sequence

Opis:

A $k$-monocore graph is a graph which has its minimum degree and degeneracy both equal to $k$. Integer sequences that can be the degree sequence of some $k$-monocore graph are characterized as follows. A nonincreasing sequence of integers $d_1, . . ., d_n$ is the degree sequence of some $k$-monocore graph $G, 0 ≤ k ≤ n − 1$, if and only if $k ≤ di ≤ min {n − 1, k + n − i}$ and $⨊d_i = 2m$, where $m$ satisfies $$\lceil\frac{k·n}{2}\rceil ≤ m ≤ k ・ n − \binom{k+1}{2}$$

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 3; 585-592
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 14.

Tytuł:

An implicit weighted degree condition for heavy cycles

Autorzy:

Cai, Junqing
Li, Hao
Ning, Wantao

Powiązania:

https://bibliotekanauki.pl/articles/30148719.pdf

Data publikacji:

2014-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

weighted graph
hamiltonian cycles
heavy cycles
implicit degree
implicit weighted degree

Opis:

For a vertex v in a weighted graph G, id^w(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a hamiltonian cycle or a cycle of weight at least 2t/3. This generalizes the result of Zhang et al. [9].

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 4; 801-810
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 15.

Tytuł:

On a Spanning $k$-Tree in which Specified Vertices Have Degree Less Than $k$

Autorzy:

Matsumura, Hajime

Powiązania:

https://bibliotekanauki.pl/articles/31339152.pdf

Data publikacji:

2015-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

spanning tree
degree bounded tree
degree sum condition

Opis:

A $k$-tree is a tree with maximum degree at most $k$. In this paper, we give a degree sum condition for a graph to have a spanning $k$-tree in which specified vertices have degree less than $k$. We denote by $\sigma_k(G)$ the minimum value of the degree sum of $k$ independent vertices in a graph $G$. Let $k ≥ 3$ and s $≥ 0$ be integers, and suppose $G$ is a connected graph and $\sigma_k(G) ≥ |V (G)|+s−1$. Then for any $s$ specified vertices, $G$ contains a spanning $k$-tree in which every specified vertex has degree less than $k$. The degree condition is sharp.

Źródło:

Discussiones Mathematicae Graph Theory; 2015, 35, 1; 191-196
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 16.

Tytuł:

3-Paths in Graphs with Bounded Average Degree

Autorzy:

Jendrol, Stanislav
Maceková, Mária
Montassier, Mickaël
Soták, Roman

Powiązania:

https://bibliotekanauki.pl/articles/31340952.pdf

Data publikacji:

2016-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

average degree
structural property
3-path
degree sequence

Opis:

In this paper we study the existence of unavoidable paths on three vertices in sparse graphs. A path uvw on three vertices u, v, and w is of type (i, j, k) if the degree of u (respectively v, w) is at most i (respectively j, k). We prove that every graph with minimum degree at least 2 and average degree strictly less than m contains a path of one of the types Moreover, no parameter of this description can be improved.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 2; 339-353
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 17.

Tytuł:

Smallest Regular Graphs of Given Degree and Diameter

Autorzy:

Knor, Martin

Powiązania:

https://bibliotekanauki.pl/articles/30147224.pdf

Data publikacji:

2014-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

regular graph
degree/diameter problem
extremal graph

Opis:

In this note we present a sharp lower bound on the number of vertices in a regular graph of given degree and diameter.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 1; 187-191
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 18.

Tytuł:

Vertex-disjoint copies of K¯₄

Autorzy:

Kawarabayashi, Ken-ichi

Powiązania:

https://bibliotekanauki.pl/articles/744487.pdf

Data publikacji:

2004

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

extremal graph theory
vertex disjoint copy
minimum degree

Opis:

Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge.
In this paper, we propose the following conjecture:
Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ.
This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.

Źródło:

Discussiones Mathematicae Graph Theory; 2004, 24, 2; 249-262
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 19.

Tytuł:

On degree sets and the minimum orders in bipartite graphs

Autorzy:

Manoussakis, Y.
Patil, H.P.

Powiązania:

https://bibliotekanauki.pl/articles/30148239.pdf

Data publikacji:

2014-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

degree sets
unicyclic graphs

Opis:

For any simple graph G, let D(G) denote the degree set ${deg_G(v) : v ∈ V (G)}$. Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y) such that D(X) = S, D(Y ) = T and the minimum orders of different types are obtained for such graphs

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 2; 383-390
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 20.

Tytuł:

Families of triples with high minimum degree are Hamiltonian

Autorzy:

Rödl, Vojtech
Ruciński, Andrzej

Powiązania:

https://bibliotekanauki.pl/articles/30148238.pdf

Data publikacji:

2014-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

3-uniform hypergraph
Hamilton cycle
minimum vertex degree

Opis:

In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least $$(\frac{5−√5}{3} + γ)\binom{n−1}{2}$$ contains a tight Hamiltonian cycle.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 2; 361-381
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 21.

Tytuł:

Equitable Coloring and Equitable Choosability of Graphs with Small Maximum Average Degree

Autorzy:

Dong, Aijun
Zhang, Xin

Powiązania:

https://bibliotekanauki.pl/articles/31342275.pdf

Data publikacji:

2018-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph coloring
equitable choosability
maximum average degree

Opis:

A graph is said to be equitably $k$-colorable if the vertex set $V (G)$ can be partitioned into $k$ independent subsets $ V_1, V_2, . . ., V_k $ such that $ | | V_i |−| V_j | | \le 1 $ $(1 \le i, j \le k) $. A graph $G$ is equitably $k$-choosable if, for any given $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $ \ceil{ \frac{|V(G)|}{ k } } $ vertices. In this paper, we prove that if $G$ is a graph such that $ mad(G) < 3 $, then $G$ is equitably $k$-colorable and equitably $k$- choosable where $ k \ge \text{max} \{ \Delta (G), 4 \} $. Moreover, if $G$ is a graph such that $ mad(G) < \frac{12}{5} $, then $G$ is equitably $k$-colorable and equitably $k$-choosable where $ k \ge \text{max} \{ \Delta (G), 3 \} $.

Źródło:

Discussiones Mathematicae Graph Theory; 2018, 38, 3; 829-839
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 22.

Tytuł:

Some applications of pq-groups in graph theory

Autorzy:

Exoo, Geoffrey

Powiązania:

https://bibliotekanauki.pl/articles/744429.pdf

Data publikacji:

2004

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

Ramsey number
edge coloring
cage
degree
girth
Cayley graph

Opis:

We describe some new applications of nonabelian pq-groups to construction problems in Graph Theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers.

Źródło:

Discussiones Mathematicae Graph Theory; 2004, 24, 1; 109-114
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 23.

Tytuł:

Large Degree Vertices in Longest Cycles of Graphs, I

Autorzy:

Li, Binlong
Xiong, Liming
Yin, Jun

Powiązania:

https://bibliotekanauki.pl/articles/31340944.pdf

Data publikacji:

2016-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

longest cycle
large degree vertices
order
connectivity
independent number

Opis:

In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 2; 363-382
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 24.

Tytuł:

On the Distance Spectral Radius of Trees with Given Degree Sequence

Autorzy:

Dadedzi, Kenneth
Misanantenaina, Valisoa Razanajatovo
Wagner, Stephan

Powiązania:

https://bibliotekanauki.pl/articles/31548271.pdf

Data publikacji:

2020-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

distance matrix
spectral radius
tree
degree sequence

Opis:

We consider the problem of maximizing the distance spectral radius and a slight generalization thereof among all trees with some prescribed degree sequence. We prove in particular that the maximum of the distance spectral radius has to be attained by a caterpillar for any given degree sequence. The same holds true for the terminal distance matrix. Moreover, we consider a generalized version of the reverse distance matrix and also study its spectral radius for trees with given degree sequence. We prove that the spectral radius is always maximized by a greedy tree. This implies several corollaries, among them a “reversed” version of a conjecture of Stevanović and Ilić. Our results parallel similar theorems for the Wiener index and other invariants.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 2; 495-524
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 25.

Tytuł:

2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices

Autorzy:

Tian, Tao
Xiong, Liming

Powiązania:

https://bibliotekanauki.pl/articles/32034090.pdf

Data publikacji:

2020-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

Hamiltonian cycle
degree sum
dominating closed trail
closure

Opis:

For a graph H, define $\overline{\sigma}_2(H)=min\{d(u)+d(v)|uv∈E(H)\}$. Let $H$ be a 2-connected claw-free simple graph of order $n$ with \(\delta(H) ≥ 3\). In [J. Graph Theory 86 (2017) 193–212], Chen proved that if $\overline{\sigma}_2(H)≥\frac{n}{2}−1$ and $n$ is sufficiently large, then $H$ is Hamiltonian with two families of exceptions. In this paper, we refine the result. We focus on the condition $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$, and characterize non-Hamiltonian 2-connected claw-free graphs $H$ of order $n$ sufficiently large with $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$. As byproducts, we prove that there are exactly six graphs in the family of 2-edge-connected triangle-free graphs of order at most seven that have no spanning closed trail and give an improvement of a result of Veldman in [Discrete Math. 124 (1994) 229–239].

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 1; 85-106
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 26.

Tytuł:

Super Edge-Connectivity and Zeroth-Order Randić Index

Autorzy:

He, Zhihong
Lu, Mei

Powiązania:

https://bibliotekanauki.pl/articles/31348172.pdf

Data publikacji:

2020-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

zeroth-order Randić index
super edge-connected
degree
triangle-free graph
minimum degree

Opis:

Define the zeroth-order Randić index as \(R^0(G)=∑_{x∈V(G)} \frac{1}{\sqrt{d_G(x)}}\), where $d_G(x)$ denotes the degree of the vertex $x$. In this paper, we present two sufficient conditions for graphs and triangle-free graphs, respectively, to be super edge-connected in terms of the zeroth-order Randić index.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 4; 971-984
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 27.

Tytuł:

A Degree Condition Implying Ore-Type Condition for Even [2, b]-Factors in Graphs

Autorzy:

Tsuchiya, Shoichi
Yashima, Takamasa

Powiązania:

https://bibliotekanauki.pl/articles/31341635.pdf

Data publikacji:

2017-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

[ a, b ]-factor
even factor
2-edge-connected
minimum degree

Opis:

For a graph $G$ and even integers $ b \ge a \ge 2 $, a spanning subgraph $F$ of $G$ such that $ a \le \text{deg}_F (x) \le b $ and $ \text{deg}_F (x) $ is even for all $ x \in V (F) $ is called an even $[a, b]$-factor of $G$. In this paper, we show that a 2-edge-connected graph $G$ of order $n$ has an even $[2, b]$-factor if $ \text{max} \{ \text{deg}_G (x) , \text{deg}_G (y) \} \ge \text{max} \{ \frac{2n}{2+b} , 3 \} $ for any nonadjacent vertices $x$ and $y$ of $G$. Moreover, we show that for $ b \ge 3a$ and $a > 2$, there exists an infinite family of 2-edge-connected graphs $G$ of order $n$ with $ \delta (G) \ge a$ such that $G$ satisfies the condition $ \text{deg}_G (x) + \text{deg}_G (y) > \frac{2an}{a+b} $ for any nonadjacent vertices $x$ and $y$ of $G$, but has no even $[a, b]$-factors. In particular, the infinite family of graphs gives a counterexample to the conjecture of Matsuda on the existence of an even $[a, b]$-factor.

Źródło:

Discussiones Mathematicae Graph Theory; 2017, 37, 3; 797-809
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 28.

Tytuł:

5-stars of low weight in normal plane maps with minimum degree 5

Autorzy:

Borodin, Oleg V.
Ivanova, Anna O.
Jensen, Tommy R.

Powiązania:

https://bibliotekanauki.pl/articles/30148303.pdf

Data publikacji:

2014-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph
plane map
vertex degree
weight
light subgraph

Opis:

It is known that there are normal plane maps $M_5$ with minimum degree 5 such that the minimum degree-sum $w(S_5)$ of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an $M_5$ has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then $w(S_5) ≤ 68$. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free $M_5$ with $w(S_5) = 48$.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 3; 539-546
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 29.

Tytuł:

Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants

Autorzy:

Das, Kinkar Ch.
Yang, Yujun
Xu, Kexiang

Powiązania:

https://bibliotekanauki.pl/articles/31340811.pdf

Data publikacji:

2016-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

resistance distance
Kirchhoff index
additive degree-Kirchhoff index
multiplicative degree-Kirchhoff index
Nordhaus-Gaddum-type result

Opis:

Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance distance-based graph invariants, namely, the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index. Some Nordhaus-Gaddum-type results for these three molecular structure descriptors are obtained. In addition, a relation between these Kirchhoffian indices is established.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 3; 695-707
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 30.

Tytuł:

Supermagic Generalized Double Graphs

Autorzy:

Ivančo, Jaroslav

Powiązania:

https://bibliotekanauki.pl/articles/31341097.pdf

Data publikacji:

2016-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

double graphs
supermagic graphs
degree-magic graphs

Opis:

A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 1; 211-225
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 31.

Tytuł:

Degree Sum Condition for the Existence of Spanning k-Trees in Star-Free Graphs

Autorzy:

Furuya, Michitaka
Maezawa, Shun-ichi
Matsubara, Ryota
Matsuda, Haruhide
Tsuchiya, Shoichi
Yashima, Takamasa

Powiązania:

https://bibliotekanauki.pl/articles/32361756.pdf

Data publikacji:

2022-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

spanning tree
k -tree
star-free
degree sum condition

Opis:

For an integer k ≥ 2, a k-tree T is defined as a tree with maximum degree at most k. If a k-tree T spans a graph G, then T is called a spanning k-tree of G. Since a spanning 2-tree is a Hamiltonian path, a spanning k-tree is an extended concept of a Hamiltonian path. The first result, implying the existence of k-trees in star-free graphs, was by Caro, Krasikov, and Roditty in 1985, and independently, Jackson and Wormald in 1990, who proved that for any integer k with k ≥ 3, every connected K_1,k-free graph contains a spanning k-tree. In this paper, we focus on a sharp condition that guarantees the existence of a spanning k-tree in K_1,k+1-free graphs. In particular, we show that every connected K_1,k+1-free graph G has a spanning k-tree if the degree sum of any 3k−3 independent vertices in G is at least |G|−2, where |G| is the order of G.

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 1; 5-13
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 32.

Tytuł:

A different short proof of Brooks theorem

Autorzy:

Rabern, Landon

Powiązania:

https://bibliotekanauki.pl/articles/31231996.pdf

Data publikacji:

2014-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

coloring
clique number
maximum degree

Opis:

Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 3; 633-634
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 33.

Tytuł:

Domination Number of Graphs with Minimum Degree Five

Autorzy:

Bujtás, Csilla

Powiązania:

https://bibliotekanauki.pl/articles/32222697.pdf

Data publikacji:

2021-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

dominating set
domination number
discharging method

Opis:

We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.

Źródło:

Discussiones Mathematicae Graph Theory; 2021, 41, 3; 763-777
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 34.

Tytuł:

On Factorable Bigraphic Pairs

Autorzy:

Yin, Jian-Hua
Li, Sha-Sha

Powiązania:

https://bibliotekanauki.pl/articles/31515537.pdf

Data publikacji:

2020-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

degree sequence
bigraphic pair
Hamiltonian cycle

Opis:

Let $S = (a_1,. . ., a_m; b_1, . . ., b_n)$, where $a_1, . . ., a_m$ and $b_1, . . ., b_n$ are two sequences of nonnegative integers. We say that $S$ is a bigraphic pair if there exists a simple bipartite graph $G$ with partite sets ${x_1, x_2, . . ., x_m}$ and ${y_1, y_2, . . ., y_n}$ such that $d_G(x_i) = a_i$ for $1 ≤ i ≤ m$ and $d_G(y_j) = b_j$ for $1 ≤ j ≤ n$. In this case, we say that $G$ is a realization of $S$. Analogous to Kundu’s $k$-factor theorem, we show that if $(a_1, a_2, . . ., a_m; b_1, b_2, . . ., b_n)$ and $(a_1 − e_1, a_2 − e_2, . . ., a_m − e_m; b_1 − f_1, b_2 − f_2, . . ., b_n − f_n)$ are two bigraphic pairs satisfying $k ≤ f_i ≤ k + 1, 1 ≤ i ≤ n$ (or$ k ≤ e_i ≤ k + 1, 1 ≤ i ≤ m$), for some $0 ≤ k ≤ m − 1$ (or $0 ≤ k ≤ n − 1$), then $(a_1, a_2, . . ., a_m; b_1, b_2, . . ., b_n)$ has a realization containing an $(e_1, e_2, . . ., e_m; f_1, f_2, . . ., f_n)$-factor. For $m = n$, we also give a necessary and sufficient condition for an $(k^n; k^n)$-factorable bigraphic pair to be connected $(k^n; k^n)$-factorable when $k ≥ 2$. This implies a characterization of bigraphic pairs with a realization containing a Hamiltonian cycle.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 3; 787-793
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 35.

Tytuł:

Describing Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree 6 or 7

Autorzy:

Batueva, Ts.Ch-D.
Borodin, O.V.
Ivanova, A.O.
Nikiforov, D.V.

Powiązania:

https://bibliotekanauki.pl/articles/32361718.pdf

Data publikacji:

2022-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

planar graph
structural properties
3-polytope
5-star
neighborhood

Opis:

In 1940, in attempts to solve the Four Color Problem, Henry Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P₅ of 3-polytopes with minimum degree 5. This description depends on 32 main parameters. (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13) Not many precise upper bounds on these parameters have been obtained as yet, even for restricted subclasses in P₅. In 2018, Borodin, Ivanova, Kazak proved that every forbidding vertices of degree from 7 to 11 results in a tight description (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6). Recently, Borodin, Ivanova, and Kazak proved every 3-polytope in P₅ with no vertices of degrees 6, 7, and 8 has a 5-vertex whose neighborhood is majorized by one of the sequences (5, 5, 5, 5, ∞) and (5, 5, 10, 5, 12), which is tight and improves a corresponding description (5, 5, 5, 5, ∞), (5, 5, 9, 5, 17), (5, 5, 10, 5, 14), (5, 5, 11, 5, 13) that follows from the Lebesgue Theorem. The purpose of this paper is to prove that every 3-polytope with minimum degree 5 and no vertices of degree 6 or 7 has a 5-vertex whose neighborhood is majorized by one of the ordered sequences (5, 5, 5, 5, ∞), (5, 5, 8, 5, 14), or (5, 5, 10, 5, 12).

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 2; 535-548
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 36.

Tytuł:

The Saturation Number for the Length of Degree Monotone Paths

Autorzy:

Caro, Yair
Lauri, Josef
Zarb, Christina

Powiązania:

https://bibliotekanauki.pl/articles/31339330.pdf

Data publikacji:

2015-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

paths
degrees
saturation

Opis:

A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known Erdős- Szekeres theorem, has been studied by the authors in two earlier papers. Here we consider a saturation problem for the parameter mp(G). We call G saturated if, for every edge e added to G, mp(G + e) > mp(G), and we define h(n, k) to be the least possible number of edges in a saturated graph G on n vertices with mp(G) < k, while mp(G+e) ≥ k for every new edge e. We obtain linear lower and upper bounds for h(n, k), we determine exactly the values of h(n, k) for k = 3 and 4, and we present constructions of saturated graphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2015, 35, 3; 557-569
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 37.

Tytuł:

On the Hypercompetition Numbers of Hypergraphs with Maximum Degree at Most Two

Autorzy:

Sano, Yoshio

Powiązania:

https://bibliotekanauki.pl/articles/31339316.pdf

Data publikacji:

2015-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
competition hypergraph
hypercompetition number

Opis:

In this note, we give an easy and short proof for the theorem by Park and Kim stating that the hypercompetition numbers of hypergraphs with maximum degree at most two is at most two.

Źródło:

Discussiones Mathematicae Graph Theory; 2015, 35, 3; 595-598
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 38.

Tytuł:

The Smallest Harmonic Index of Trees with Given Maximum Degree

Autorzy:

Rasi, Reza
Sheikholeslami, Seyed Mahmoud

Powiązania:

https://bibliotekanauki.pl/articles/31342320.pdf

Data publikacji:

2018-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

harmonic index
trees

Opis:

The harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T.

Źródło:

Discussiones Mathematicae Graph Theory; 2018, 38, 2; 499-513
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 39.

Tytuł:

A Homotopy Approach to Rational Covariance Extension With Degree Constraint

Autorzy:

Enqvist, P.

Powiązania:

https://bibliotekanauki.pl/articles/908061.pdf

Data publikacji:

2001

Wydawca:

Uniwersytet Zielonogórski. Oficyna Wydawnicza

Tematy:

optymalizacja
teoria systemów
stochastic realization theory
rational covariance extension problem
ARMA model design
continuation method
optimization

Opis:

The solutions to the Rational Covariance Extension Problem (RCEP) are parameterized by the spectral zeros. The rational filter with a specified numerator solving the RCEP can be determined from a known convex optimization problem. However, this optimization problem may become ill-conditioned for some parameter values. A modification of the optimization problem to avoid the ill-conditioning is proposed and the modified problem is solved efficiently by a continuation method.

Źródło:

International Journal of Applied Mathematics and Computer Science; 2001, 11, 5; 1173-1201
1641-876X
2083-8492

Pojawia się w:

International Journal of Applied Mathematics and Computer Science

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 40.

Tytuł:

Low 5-Stars at 5-Vertices in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree from 7 to 9

Autorzy:

Borodin, Oleg V.
Bykov, Mikhail A.
Ivanova, Anna O.

Powiązania:

https://bibliotekanauki.pl/articles/31348144.pdf

Data publikacji:

2020-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

planar map
planar graph
3-polytope
structural properties
5-star
weight
height

Opis:

In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class $P_5$ of 3-polytopes with minimum degree 5. Given a 3-polytope $P$, by $h_5(P)$ we denote the minimum of the maximum degrees (height) of the neighborhoods of 5-vertices (minor 5-stars) in $P$. Recently, Borodin, Ivanova and Jensen showed that if a polytope $P$ in $P_5$ is allowed to have a 5-vertex adjacent to two 5-vertices and two more vertices of degree at most 6, called a (5, 5, 6, 6, ∞)-vertex, then $h_5(P)$ can be arbitrarily large. Therefore, we consider the subclass \(P_5^\ast\) of 3-polytopes in $P_5$ that avoid (5, 5, 6, 6, ∞)-vertices. For each $P^\ast$ in $P_5^\ast$ without vertices of degree from 7 to 9, it follows from Lebesgue’s Theorem that $h_5(P^\ast) ≤ 17$. Recently, this bound was lowered by Borodin, Ivanova, and Kazak to the sharp bound $h_5(P^\ast) ≤ 15$ assuming the absence of vertices of degree from 7 to 11 in $P^\ast$. In this note, we extend the bound $h_5(P^\ast) ≤ 15$ to all $P^\ast$s without vertices of degree from 7 to 9.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1025-1033
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 41.

Tytuł:

On the Rainbow Vertex-Connection

Autorzy:

Li, Xueliang
Shi, Yongtang

Powiązania:

https://bibliotekanauki.pl/articles/30146636.pdf

Data publikacji:

2013-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

rainbow vertex-connection
vertex coloring
minimum degree
2-step dominating set

Opis:

A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. It was proved that if $G$ is a graph of order $n$ with minimum degree $ \delta $, then $ rvc(G) < 11n//\delta$. In this paper, we show that $rvc(G) \le 3n//(δ+1)+5$ for $ \delta \ge \sqrt{n-1} -1 $ and $ n \le 290 $, while $ rvc(G) \le 4n//(δ + 1) + 5 $ for $ 16 \le \delta \le \sqrt{n-1}-2 $ and $ rvc(G) \le 4n//(\delta + 1) + C(\delta) $ for $6 \le \delta \le 15$, where $ C(\delta) = e^\frac{ 3 \log (\delta^3 + 2 \delta^2 +3)-3(\log 3 - 1)}{\delta - 3} - 2$. We also prove that $ rvc(G) \le 3n//4 − 2 $ for $ \delta = 3$, $ rvc(G) \le 3n//5 − 8//5$ for $\delta = 4$ and $rvc(G) \le n//2 − 2$ for $\delta = 5$. Moreover, an example constructed by Caro et al. shows that when $ \delta \ge \sqrt{n-1} - 1 $ and $ \delta = 3, 4, 5 $, our bounds are seen to be tight up to additive constants.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 2; 307-313
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 42.

Tytuł:

Trees Whose Even-Degree Vertices Induce a Path are Antimagic

Autorzy:

Lozano, Antoni
Mora, Mercè
Seara, Carlos
Tey, Joaquín

Powiązania:

https://bibliotekanauki.pl/articles/32304141.pdf

Data publikacji:

2022-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

antimagic labeling
tree

Opis:

An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . ., |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Anti-magic labeling of trees, Discrete Math. 331 (2014) 9–14].

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 3; 959-966
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 43.

Tytuł:

Linear List Coloring of Some Sparse Graphs

Autorzy:

Chen, Ming
Li, Yusheng
Zhang, Li

Powiązania:

https://bibliotekanauki.pl/articles/32083756.pdf

Data publikacji:

2021-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

linear coloring
maximum average degree
planar graphs
discharging

Opis:

A linear $k$-coloring of a graph is a proper $k$-coloring of the graph such that any subgraph induced by the vertices of any pair of color classes is a union of vertex-disjoint paths. A graph $G$ is linearly $L$-colorable if there is a linear coloring $c$ of $G$ for a given list assignment $L = \{L(v) : v ∈ V(G)\}$ such that $c(v) ∈ L(v)$ for all $v ∈ V(G)$, and $G$ is linearly $k$-choosable if $G$ is linearly $L$-colorable for any list assignment with $|L(v)| ≥ k$. The smallest integer $k$ such that $G$ is linearly $k$-choosable is called the linear list chromatic number, denoted by $lc_l(G)$. It is clear that \(lc_l(G)≥\Big\lceil\frac{\Delta(G)}{1}\Big\rceil+1\) for any graph $G$ with maximum degree $\Delta(G)$. The maximum average degree of a graph $G$, denoted by $mad(G)$, is the maximum of the average degrees of all subgraphs of $G$. In this note, we shall prove the following. Let $G$ be a graph, (1) if $mad(G)<\frac{8}{3}$ and $\Delta(G) ≥ 7$, then \(lc_l(G)=\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+1\); (2) if $mad(G)<{18}{7}$ and $\Delta(G) ≥ 5$, then \(lc_l(G)=\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+1\); (3) if $mad(G)<{20}{7}$ and $\Delta(G) ≥ 5$, then \(lc_l(G)≤\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+2\).

Źródło:

Discussiones Mathematicae Graph Theory; 2021, 41, 1; 51-64
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 44.

Tytuł:

The Bipartite-Splittance of a Bipartite Graph

Autorzy:

Yin, Jian-Hua
Guan, Jing-Xin

Powiązania:

https://bibliotekanauki.pl/articles/31343732.pdf

Data publikacji:

2019-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

degree sequence pair
bipartite-split graph
bipartite-splittance

Opis:

A bipartite-split graph is a bipartite graph whose vertex set can be partitioned into a complete bipartite set and an independent set. The bipartite- splittance of an arbitrary bipartite graph is the minimum number of edges to be added or removed in order to produce a bipartite-split graph. In this paper, we show that the bipartite-splittance of a bipartite graph depends only on the degree sequence pair of the bipartite graph, and an easily computable formula for it is derived. As a corollary, a simple characterization of the degree sequence pair of bipartite-split graphs is also given.

Źródło:

Discussiones Mathematicae Graph Theory; 2019, 39, 1; 23-29
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 45.

Tytuł:

Eccentricity of Networks with Structural Constraints

Autorzy:

Krnc, Matjaž
Sereni, Jean-Sébastien
Škrekovski, Riste
Yilma, Zelealem B.

Powiązania:

https://bibliotekanauki.pl/articles/31348091.pdf

Data publikacji:

2020-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

eccentricity
network
bipartite graph
complex network
maximum degree

Opis:

The eccentricity of a node v in a network is the maximum distance from v to any other node. In social networks, the reciprocal of eccentricity is used as a measure of the importance of a node within a network. The associated centralization measure then calculates the degree to which a network is dominated by a particular node. In this work, we determine the maximum value of eccentricity centralization as well as the most centralized networks for various classes of networks including the families of bipartite networks (two-mode data) with given partition sizes and tree networks with fixed number of nodes and fixed maximum degree. To this end, we introduce and study a new way of enumerating the nodes of a tree which might be of independent interest.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1141-1162
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 46.

Tytuł:

Incidence Coloring—Cold Cases

Autorzy:

Kardoš, František
Maceková, Mária
Mockovčiaková, Martina
Sopena, Éric
Soták, Roman

Powiązania:

https://bibliotekanauki.pl/articles/32083735.pdf

Data publikacji:

2020-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

incidence coloring
incidence chromatic number
planar graph
maximum average degree

Opis:

An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident to v. Two incidences (v, e) and (u, f) are adjacent if at least one of the following holds: (i) v = u, (ii) e = f, or (iii) edge vu is from the set {e, f}. An incidence coloring of G is a coloring of its incidences assigning distinct colors to adjacent incidences. The minimum number of colors needed for incidence coloring of a graph is called the incidence chromatic number. It was proved that at most Δ(G) + 5 colors are enough for an incidence coloring of any planar graph G except for Δ(G) = 6, in which case at most 12 colors are needed. It is also known that every planar graph G with girth at least 6 and Δ(G) ≥ 5 has incidence chromatic number at most Δ(G) + 2. In this paper we present some results on graphs regarding their maximum degree and maximum average degree. We improve the bound for planar graphs with Δ(G) = 6. We show that the incidence chromatic number is at most Δ(G) + 2 for any graph G with mad(G) < 3 and Δ(G) = 4, and for any graph with mad(G)<103 and Δ(G) ≥ 8.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 1; 345-354
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 47.

Tytuł:

Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph

Autorzy:

Stanić, Zoran

Powiązania:

https://bibliotekanauki.pl/articles/32304147.pdf

Data publikacji:

2022-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

(net) Laplacian matrix
edge perturbations
largest eigenvalue
net-degree

Opis:

Given a signed graph $ \dot{G} $, let $ A_{ \dot{G} } $ and $ D_{\dot{G}}^\pm $ denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of $ \dot{G} $ is defined to be $ N_{ \dot{G} } = D_{\dot{G}}^\pm - A_{ \dot{G} } $. In this study we give some properties of the eigenvalues of $ N_{ \dot{G} } $. In particular, we consider their behaviour under some edge perturbations, establish some relations between them and the eigenvalues of the standard Laplacian matrix and give some lower and upper bounds for the largest eigenvalue of $ N_{ \dot{G} } $.

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 3; 893-903
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 48.

Tytuł:

Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten

Autorzy:

Dong, Aijun
Li, Tong

Powiązania:

https://bibliotekanauki.pl/articles/32227944.pdf

Data publikacji:

2021-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

total coloring
neighbor product distinguishing coloring
planar graph

Opis:

A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . ., k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u. For each edge uv ∈ E(G), if p(u) ≠ p(v), then we say the coloring c distinguishes adjacent vertices by product and call it a neighbor product distinguishing k-total coloring of G. By X^″_∏(G), we denote the smallest value of k in such a coloring of G. It has been conjectured by Li et al. that Δ(G) + 3 colors enable the existence of a neighbor product distinguishing total coloring. In this paper, by applying the Combinatorial Nullstellensatz, we obtain that the conjecture holds for planar graph with Δ(G) ≥ 10. Moreover, for planar graph G with Δ(G) ≥ 11, it is neighbor product distinguishing (Δ(G) + 2)-total colorable, and the upper bound Δ(G) + 2 is tight.

Źródło:

Discussiones Mathematicae Graph Theory; 2021, 41, 4; 981-999
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 49.

Tytuł:

Decomposition of the Product of Cycles Based on Degree Partition

Autorzy:

Borse, Y. M.
Shaikh, S. R.

Powiązania:

https://bibliotekanauki.pl/articles/31343576.pdf

Data publikacji:

2019-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

hypercube
Cartesian product
n-connected
regular
bipan- cyclic
spanning subgraph

Opis:

The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n₁+ n₂+ ・ ・ ・ + n_k with k ≥ 2 and n_i ≥ 2 for each i. We prove that if k = 2, then G can be decomposed into two spanning subgraphs G₁ and G₂ such that each G_i is n_i-regular, n_i-connected, and bipancyclic or nearly bipancyclic. For k > 2, we establish that if all n_i in the partition of 2n are even, then G can be decomposed into k spanning subgraphs G₁, G₂, . . ., G_k such that each G_i is n_i-regular and n_i-connected. These results are analogous to the corresponding results for hypercubes.

Źródło:

Discussiones Mathematicae Graph Theory; 2019, 39, 1; 241-256
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 50.

Tytuł:

Equating κ Maximum Degrees in Graphs without Short Cycles

Autorzy:

Fürst, Maximilian
Gentner, Michael
Jäger, Simon
Rautenbach, Dieter
Henning, Michael A.

Powiązania:

https://bibliotekanauki.pl/articles/31523205.pdf

Data publikacji:

2020-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

maximum degree
repeated degrees
repetition number

Opis:

For an integer $k$ at least 2, and a graph $G$, let $f_k(G)$ be the minimum cardinality of a set $X$ of vertices of $G$ such that $G − X$ has either $k$ vertices of maximum degree or order less than $k$. Caro and Yuster [Discrete Mathematics 310 (2010) 742–747] conjectured that, for every $k$, there is a constant $c_k$ such that \(f_k(G)≤c_k\sqrt{n(G)}\) for every graph $G$. Verifying a conjecture of Caro, Lauri, and Zarb [arXiv:1704.08472v1], we show the best possible result that, if t is a positive integer, and $F$ is a forest of order at most \(1/6(t^3+6t^2+17t+12)\), then $f_2(F) ≤ t$. We study $f_3(F)$ for forests $F$ in more detail obtaining similar almost tight results, and we establish upper bounds on $f_k(G)$ for graphs $G$ of girth at least 5. For graphs $G$ of girth more than $2p$, for $p$ at least 3, our results imply \(f_k(G)=O\bigg(n(G)\frac{p+1}{3_p}\bigg)\). Finally, we show that, for every fixed $k$, and every given forest $F$, the value of $f_k(F)$ can be determined in polynomial time.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 3; 841-853
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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