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Wyświetlanie 1-15 z 68
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
Artykuł
Tytuł:
Universality in Graph Properties with Degree Restrictions
Autorzy:
Broere, Izak
Heidema, Johannes
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/30146518.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
countable graph
universal graph
induced-hereditary
k-degenerate graph
graph with colouring number at most k + 1
graph property with assignment
Opis:
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set ℐc of all countable graphs (since every graph in ℐc is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of ℐc is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 477-492
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
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
Artykuł
Tytuł:
The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination
Autorzy:
Amos, David
Asplund, John
Brimkov, Boris
Davila, Randy
Powiązania:
https://bibliotekanauki.pl/articles/32083827.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Slater number
domination number
sub- k -domination number
k -domination number
degree sequence index strategy
Opis:
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide structural results on sub-k-domination, and explore properties of graphs which are subk(G)-critical with respect to addition and deletion of vertices and edges.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 209-225
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Tytuł:
The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7
Autorzy:
Sun, Lin
Wu, Jianliang
Wang, Bing
Liu, Bin
Powiązania:
https://bibliotekanauki.pl/articles/31348158.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
list edge coloring
list total coloring
Opis:
A graph $G$ is edge $k$-choosable (respectively, total $k$-choosable) if, whenever we are given a list $L(x)$ of colors with $|L(x)| = k$ for each $x ∈ E(G) (x ∈ E(G) ∪ V (G))$, we can choose a color from $L(x)$ for each element $x$ such that no two adjacent (or incident) elements receive the same color. The list edge chromatic index $χ_l^′(G)$ (respectively, the list total chromatic number $χ_l^{′′}(G))$ of $G$ is the smallest integer $k$ such that $G$ is edge (respectively, total) $k$-choosable. In this paper, we focus on a planar graph $G$, with maximum degree $Δ (G) ≥ 7$ and with some structural restrictions, satisfies $χ_l^′(G) = Δ (G)$ and $χ_l^{′′}(G) = Δ (G) + 1$.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1005-1024
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
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
Artykuł
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
Artykuł
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
Artykuł
Tytuł:
Spectral Radius and Hamiltonicity of Graphs
Autorzy:
Yu, Guidong
Fang, Yi
Fan, Yizheng
Cai, Gaixiang
Powiązania:
https://bibliotekanauki.pl/articles/31343181.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
spectral radius
singless Laplacian spectral radius
traceable
Hamiltonian-connected
traceable from every vertex
minimum degree
Opis:
In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or its complement, respectively. Secondly, we give the conditions for a nearly balanced bipartite graph to be traceable in terms of spectral radius, signless Laplacian spectral radius of the graph or its quasi-complement, respectively.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 951-974
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Autorzy:
Liu, Weijun
Liu, Minmin
Zhang, Pengli
Feng, Lihua
Powiązania:
https://bibliotekanauki.pl/articles/32083834.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
spectral radius
minimum degree
k -Hamiltonian
k -path-coverable
Opis:
A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths. In this paper, by making use of the vertex degree sequence and an appropriate closure concept (due to Bondy and Chvátal), we present sufficient spectral conditions of a connected graph with fixed minimum degree and large order to be k-Hamiltonian or k-path-coverable.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 161-179
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
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
Artykuł
Wyświetlanie 1-15 z 68

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