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2008

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

8 years 5 months ago
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) ...
Flavia Bonomo, Maria Chudnovsky, Guillermo Dur&aac
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DAM
Authors Flavia Bonomo, Maria Chudnovsky, Guillermo Durán
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