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Wyświetlanie 1-10 z 20
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, idw(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
Artykuł
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
Artykuł
Tytuł:
On traceability and 2-factors in claw-free graphs
Autorzy:
Fronček, Dalibor
Ryjáček, Zdeněk
Skupień, Zdzisław
Powiązania:
https://bibliotekanauki.pl/articles/744410.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
traceability
2-factor
claw
degree condition
closure
Opis:
If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σₖ > n + k² - 4k + 7 (where k is an arbitrary constant), then G has a 2-factor with at most k - 1 components. As a second main result, we present classes of graphs ₁,...,₈ such that every sufficiently large connected claw-free graph satisfying degree condition σ₆(k) > n + 19 (or, as a corollary, δ(G) > (n+19)/6) either belongs to $⋃ ⁸_{i=1} _i$ or is traceable.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 55-71
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On distance local connectivity and vertex distance colouring
Autorzy:
Holub, Přemysl
Powiązania:
https://bibliotekanauki.pl/articles/743741.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
degree condition
distance local connectivity
distance chromatic number
Opis:
In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 209-227
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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 K1,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 K1,k+1-free graphs. In particular, we show that every connected K1,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
Artykuł
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
Artykuł
Tytuł:
A σ₃ type condition for heavy cycles in weighted graphs
Autorzy:
Zhang, Shenggui
Li, Xueliang
Broersma, Hajo
Powiązania:
https://bibliotekanauki.pl/articles/743462.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weighted graph
(long, heavy, Hamilton) cycle
weighted degree
(weighted) degree sum
Opis:
A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree $d^w(v)$ of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz) for every vertex z ∈ N(x)∩N(y) with d(x,y) = 2; 3. 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 Hamilton cycle or a cycle of weight at least 2m/3. This generalizes a theorem of Fournier and Fraisse on the existence of long cycles in k-connected unweighted graphs in the case k = 2. Our proof of the above result also suggests a new proof to the theorem of Fournier and Fraisse in the case k = 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 2; 159-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Infestation Degree of Trees with Common Mistletoe Viscum album L. and their Health Status (on the Example of Praszka City)
Autorzy:
Gołąbek, E.
Sławiński, J.
Powiązania:
https://bibliotekanauki.pl/articles/123572.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Inżynierii Ekologicznej
Tematy:
Viscum album L.
common mistletoe
degree of trees settlement
health condition of trees
Praszka
Opis:
The research was carried out in September and October 2013. Their main aim was to obtain the information on the abundance and distribution of the common mistletoe in Praszka, assess the health status of the trees infested with this semi-parasite, and to determine its impact on the health of the hosts. All the trees with mistletoe were examined (in terms of the species, the number of semiparasite shrubs, the host health). The distribution and density hosts were presented on a prepared network with an area of 1 ha and Pearson’s correlation factor was used to determine the relationship between the infestation degree of a host and its state of health. Only the typical subspecies of mistletoe – Viscum album L. subsp. album, which occupied 11 species of trees were found in the city of Praszka. These were mainly: black poplar Populus nigra L., small-leaved lime Tilia cordata L. and black locust Robinia pseudoacacia L. (they are also the most common or the frequent hosts in the country). The distribution of mistletoe in the city is uneven, and this is mainly due to the degree of urbanization, sunshine, noise, occurrence of the most common hosts as well as the presence of birds. It turned out that the largest groups of hosts were located along the roads in low building areas, on the peripheries of the city as well as in parks and cemeteries. The health condition of trees inhabited by mistletoe was generally good. There was a correlation between the number of mistletoe shrubs on the host and its health status (the greater the number of shrubs, the worse the health status of the host).
Źródło:
Journal of Ecological Engineering; 2017, 18, 6; 80-85
2299-8993
Pojawia się w:
Journal of Ecological Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Diagnosis of the Technical Condition of Historic Tenement Houses as the First Stage of Revitalisation of the City
Autorzy:
Nowogońska, Beata
Powiązania:
https://bibliotekanauki.pl/articles/1838068.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
revitalisation
technical condition assessment
technical wear degree
historic buildings
rewitalizacja
ocena stanu technicznego
stopień zużycia technicznego
budynki historyczne
Opis:
Revitalisation of degraded downtown areas is a problem for many cities and towns in Europe. All spatial, economic and social changes result from the expectations of residents together with technical needs. The scope of revitalisation activities results from the diagnosis of the technical condition of the degraded part of the city. The article presents a sample assessment of the technical condition of a tenement house in Kożuchów located within a downtown complex covered by revitalisation plans.
Źródło:
Civil and Environmental Engineering Reports; 2020, 30, 4; 102-110
2080-5187
2450-8594
Pojawia się w:
Civil and Environmental Engineering Reports
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variations on a sufficient condition for Hamiltonian graphs
Autorzy:
Ainouche, Ahmed
Lapiquonne, Serge
Powiązania:
https://bibliotekanauki.pl/articles/743758.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycles
partially square graph
degree sum
independent sets
neighborhood unions and intersections
dual closure
Opis:
Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding edges uv whenever the vertices u,v have a common neighbor x satisfying the condition $N_G(x) ⊆ N_G[u] ∪ N_G[v]$, where $N_G[x] = N_G(x) ∪ {x}$. In particular, this condition is satisfied if x does not center a claw (an induced $K_{1,3}$). Clearly G ⊆ G* ⊆ G², where G² is the square of G. For any independent triple X = {x,y,z} we define
σ̅(X) = d(x) + d(y) + d(z) - |N(x) ∩ N(y) ∩ N(z)|.
Flandrin et al. proved that a 2-connected graph G is hamiltonian if [σ̅]₃(X) ≥ n holds for any independent triple X in G. Replacing X in G by X in the larger graph G*, Wu et al. improved recently this result. In this paper we characterize the nonhamiltonian 2-connected graphs G satisfying the condition [σ̅]₃(X) ≥ n-1 where X is independent in G*. Using the concept of dual closure we (i) give a short proof of the above results and (ii) we show that each graph G satisfying this condition is hamiltonian if and only if its dual closure does not belong to two well defined exceptional classes of graphs. This implies that it takes a polynomial time to check the nonhamiltonicity or the hamiltonicity of such G.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 229-240
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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