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Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs

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2008-04-01
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Bonomo, Flavia
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Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs
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Author
  • Bonomo, Flavia;
  • Chudnovsky, Maria;
  • Durán Maggiolo, Guillermo;
Abstract
A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs.
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URI: https://repositorio.uchile.cl/handle/2250/125073
DOI: 10.1016/j.dam.2007.05.048
ISSN: 0166-218X
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DISCRETE APPLIED MATHEMATICS Volume: 156 Issue: 7 Pages: 1058-1082 Published: APR 1 2008
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