Matchings in infinite graphs
P. J. McCarthy (1978)
Czechoslovak Mathematical Journal
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P. J. McCarthy (1978)
Czechoslovak Mathematical Journal
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Babel, Luitpold, Brandstädt, Andreas, Le, Van Bang (2002)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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P. Dankelmann, Henda C. Swart, P. van den Berg, Wayne Goddard, M. D. Plummer (2008)
Czechoslovak Mathematical Journal
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A graph is a minimal claw-free graph (m.c.f. graph) if it contains no (claw) as an induced subgraph and if, for each edge of , contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.
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 , where is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.
Little, C., Vince, A. (2006)
The Electronic Journal of Combinatorics [electronic only]
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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 and five edges . 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...