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

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. Key words: Claw-free graphs, clique-perfect graphs, hereditary clique-Helly graphs, line graphs, perfect graphs. ded abstract of this paper was presented at GRACO 2005 (2nd Brazilian Symposium on Graphs, Algorithms, and Combinatorics) ...

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Flavia Bonomo, Maria Chudnovsky, Guillermo Durán
• Keywords: Claw-free Graphs, Clique-perfect Graphs, DAM 2008, Maximum Clique-independent Set