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2008

Partial characterizations of clique-perfect and coordinated graphs: superclasses of triangle-free graphs

8 years 3 months ago
Partial characterizations of clique-perfect and coordinated graphs: superclasses of triangle-free graphs
A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color equals the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The complete lists of minimal forbidden induced subgraphs for the classes of clique-perfect and coordinated graphs are not known, but some partial characterizations have been obtained. In this paper, we characterize cliqueperfect and coordinated graphs by minimal forbidden induced subgraphs when the graph is either paw-free or {gem,W4,bull}-free, both superclasses of triangle-free graphs. Key words: Clique-perfect graphs, coordinated graphs, {gem,W4,bull}-free graphs, paw-fre...
Flavia Bonomo, Guillermo Durán, Francisco J
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where ENDM
Authors Flavia Bonomo, Guillermo Durán, Francisco J. Soulignac, Gabriel Sueiro
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