Temat: edge-connectivity - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Minimum Edge Cuts in Diameter 2 Graphs
Autorzy:: Bickle, Allan
Schwenk, Allen
Tematy:: edge connectivity
diameter; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31343375.pdf Link otwiera się w nowym oknie
Opis:: Plesnik proved that the edge connectivity and minimum degree are equal for diameter 2 graphs. We provide a streamlined proof of this fact and characterize the diameter 2 graphs with a nontrivial minimum edge cut.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 2.

Tytuł:: A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs
Autorzy:: Sun, Yuefang
Tematy:: generalized connectivity
generalized edge-connectivity
strong product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341589.pdf Link otwiera się w nowym oknie
Opis:: The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$, mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized $k$-edge-connectivity which is defined as $ \lambda_k (G) = \text{min} \{ \lambda_G (S) | S \subseteq V (G) $ and $ |S| = k \} $, where $ \lambda_G (S) $ denote the maximum number $ \mathcal{l} $ of pairwise edge-disjoint trees $ T_1 $, $ T_2 $, . . ., $ T_\mathcal{l} $ in $G$ such that $S \subseteq V (T_i)$ for $ 1 \le i \le \mathcal{l} $. In this paper we get a sharp lower bound for the generalized 3-edge-connectivity of the strong product of any two connected graphs.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 3.

Tytuł:: Graphs with Large Generalized (Edge-)Connectivity
Autorzy:: Li, Xueliang
Mao, Yaping
Tematy:: (edge-)connectivity
Steiner tree
internally disjoint trees
edge-disjoint trees
packing
generalized (edge-)connectivity; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31340594.pdf Link otwiera się w nowym oknie
Opis:: The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $ \lambda_k (G)$. In this paper, graphs of order $n$ such that $ \kappa_k (G) = n - k/2 - 1 $ and $ \lambda_k (G) = n - k/2 - 1 $ for even $k$ are characterized.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 4.

Tytuł:: Corrigendum to "Minimum edge cuts in diameter 2 graphs"
Autorzy:: Bickle, Allan
Schwenk, Allen
Tematy:: edge connectivity
diameter; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/59974134.pdf Link otwiera się w nowym oknie
Opis:: In [Minimum edge cuts in diameter $2$ graphs, Discuss. Math. Graph Theory 39 (2) (2019) 605–608] we proved several results on the structure of diameter 2 graphs with a nontrivial minimum edge cut. An error led to several results being incorrect. Here we state and prove the corresponding correct results.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 5.

Tytuł:: Cospectral Pairs of Regular Graphs with Different Connectivity
Autorzy:: Haemers, Willem H.
Tematy:: graph spectrum
vertex-connectivity
edge-connectivity
spectral characterization; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31552242.pdf Link otwiera się w nowym oknie
Opis:: For vertex- and edge-connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 6.

Tytuł:: The Minimum Size of a Graph with Given Tree Connectivity
Autorzy:: Sun, Yuefang
Sheng, Bin
Jin, Zemin
Tematy:: generalized connectivity
tree connectivity
eneralized k-connectivity
generalized k-edge-connectivity
packing; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32083875.pdf Link otwiera się w nowym oknie
Opis:: For a graph $G = (V, E)$ and a set $S ⊆ V$ of at least two vertices, an $S$-tree is a such subgraph $T$ of $G$ that is a tree with $S ⊆ V(T)$. Two $S$-trees $T_1$ and $T_2$ are said to be internally disjoint if $E(T_1) ∩ E(T_2) = ∅$ and $V(T_1) ∩ V(T_2) = S$, and edge-disjoint if $E(T_1) ∩ E(T_2) = ∅$. The generalized local connectivity $κ_G(S)$ (generalized local edge-connectivity $λ_G(S)$, respectively) is the maximum number of internally disjoint (edge-disjoint, respectively) $S$-trees in $G$. For an integer $k$ with $2 ≤ k ≤ n$, the generalized $k$-connectivity (generalized $k$-edge-connectivity, respectively) is defined as $κ_k(G) = min{κ_G(S) | S ⊆ V(G), |S| = k} (λ_k(G) = min{λ_G(S) | S ⊆ V(G), |S| = k}$, respectively). Let $f(n, k, t)$ ($g(n, k, t)$, respectively) be the minimum size of a connected graph $G$ with order $n$ and $κ_k(G) = t$ ($λ_k(G) = t$, respectively), where $3 ≤ k ≤ n$ and $1≤t≤n-⌈\frac{k}{2}⌉$. For general $k$ and $t$, Li and Mao obtained a lower bound for $g(n, k, t)$ which is tight for the case $k = 3$. We show that the bound also holds for $f(n, k, t)$ and is tight for the case $k = 3$. When t is general, we obtain upper bounds of both $f(n, k, t)$ and $g(n, k, t)$ for $k ∈ {3, 4, 5}$, and all of these bounds can be attained. When $k$ is general, we get an upper bound of $g(n, k, t)$ for $t ∈ {1, 2, 3, 4}$ and an upper bound of $f(n, k, t)$ for $t ∈ {1, 2, 3}$. Moreover, both bounds can be attained.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 7.

Tytuł:: More on even [a,b]-factors in graphs
Autorzy:: Khodkar, Abdollah
Xu, Rui
Tematy:: [a,b]-factor
spanning graph
edge-connectivity; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743747.pdf Link otwiera się w nowym oknie
Opis:: In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the order of graphs.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 8.

Tytuł:: Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:: Volkmann, Lutz
Tematy:: edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31343389.pdf Link otwiera się w nowym oknie
Opis:: Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 9.

Tytuł:: Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs
Autorzy:: Sun, Yuefang
Tematy:: generalized edge-connectivity
Cartesian product
strong product
lexicographic product; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31340760.pdf Link otwiera się w nowym oknie
Opis:: The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$ was introduced by Hager in 1985. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized $k$-edge-connectivity which is defined as $ \lambda k(G) = \text{min} \{ \lambda (S) : S \subseteq V (G) \text{ and } |S| = k \} $, where $ \lambda(S) $ denote the maximum number $ \mathcal{l} $ of pairwise edge-disjoint trees $ T_1, T_2, . . ., T_\mathcal{l} $ in $G$ such that $ S \subseteq V ( T_i ) $ for $ 1 \le i \le \mathcal{l} $. In this paper, we study the generalized edge- connectivity of product graphs and obtain sharp upper bounds for the generalized 3-edge-connectivity of Cartesian product graphs and strong product graphs. Among our results, some special cases are also discussed.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 10.

Tytuł:: A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected
Autorzy:: Wang, Shiying
Wang, Meiyu
Zhang, Lei
Tematy:: graph
neighborhood
k -restricted edge connectivity
super k -restricted edge connected graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341790.pdf Link otwiera się w nowym oknie
Opis:: For a subset $S$ of edges in a connected graph $G$, $S$ is a $k$-restricted edge cut if $G − S$ is disconnected and every component of $G − S$ has at least $k$ vertices. The $k$-restricted edge connectivity of $G$, denoted by $ \lambda_k (G) $, is defined as the cardinality of a minimum $k$-restricted edge cut. Let $ \xi_k(G) = \text{min} \{ | [ X , \overline{X} ] | : |X| = k, G[X] $ is connected $ \} $, where $ \overline{X} = V (G) \backslash X $. A graph $G$ is super $k$-restricted edge connected if every minimum $k$-restricted edge cut of $G$ isolates a component of order exactly $k$. Let $k$ be a positive integer and let $G$ be a graph of order $ \nu \ge 2k$. In this paper, we show that if $ | N( u ) \cup N( v ) | \ge k +1 $ for all pairs $u$, $v$ of nonadjacent vertices and $ \xi_k (G) \le \floor{ ν/2}+k $, then $G$ is super $k$-restricted edge connected.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Informacja

Wyszukujesz frazę "edge-connectivity" wg kryterium: Temat