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Displaying similar documents to “Matchings in infinite graphs”

On a generalization of perfect b -matching

Ľubica Šándorová, Marián Trenkler (1991)

Mathematica Bohemica

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The paper is concerned with the existence of non-negative or positive solutions to A f = β , where A is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.

On the total domination subdivision numbers in graphs

Seyed Sheikholeslami (2010)

Open Mathematics

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A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Karami, Khoeilar, Sheikholeslami and Khodkar,...

The perfection and recognition of bull-reducible Berge graphs

Hazel Everett, Celina M. H. de Figueiredo, Sulamita Klein, Bruce Reed (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The recently announced Strong Perfect Graph Theorem states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x , a , b , c , d and five edges x a , x b , a b , a d , b c . A graph is bull-reducible if no vertex is in two bulls. In this paper we give a simple proof that every bull-reducible Berge graph is perfect. Although this result follows...