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Toughness and matching extension in graphs

โœ Scribed by M.D. Plummer


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
588 KB
Volume
72
Category
Article
ISSN
0012-365X

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๐Ÿ“œ SIMILAR VOLUMES


Binding number and toughness for matchin
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A graph G of even order is said to be k-extendable if every matching of size k in G can be extended to a 1-factor of G. Plummet (1988) showed that a graph G is k-extendable if tough (G) > k, and we here prove that G is also k-extendable if bind(G) > max {k, (7k + 13)/12}.

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The matching graph M (G) of a graph G is that graph whose vertices are the maximum matchings in G and where two vertices M 1 and M 2 of M (G) this graph models a metric space whose metric is defined on the set of maximum matchings in G. Which graphs are matching graphs of some graph is not known in

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Let G = ( Y E ) be an undirected graph. A subset F of E is a matching cutset of G if no two edges of Fare incident with the same point, and G-F has more components than G. ChGatal [2] proved that it is NP-complete to recognize graphs with a matching cutset even if the input is restricted to graphs w

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## Abstract The matching polynomial ฮฑ(__G, x__) of a graph __G__ is a form of the generating function for the number of sets of __k__ independent edges of __G__. in this paper we show that if __G__ is a graph with vertex __v__ then there is a tree __T__ with vertex __w__ such that \documentclass{ar