Characterization and recognition of Helly circular-arc clique-perfect graphs

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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. A graph G is clique-perfect if the sizes of a minimum clique-transversal and a maximum clique-independent set 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. Another open question concerning clique-perfect graphs is the complexity of the recognition problem. In this work we characterize clique-perfect graphs by a restricted list of minimal forbidden induced subgraphs when the graph is a Helly circular-arc graph. This characterization leads to a polynomial time recognition algorithm for clique-perfect graphs inside this class of graphs.

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Cited by (1)

  • Partial characterizations of clique-perfect graphs II: Diamond-free and Helly circular-arc graphs

    2009, Discrete Mathematics
    Citation Excerpt :

    An interesting survey on graph classes can be found in [27]. Preliminary results of this paper were published in [5,7]. [8]

1

Partially supported by UBACyT Grant X184, PICT ANPCyT Grant 11-09112 and PID Conicet Grant 644/98, Argentina and CNPq under PROSUL project Proc. 490333/2004-4, Brazil.

2

Partially supported by FONDECyT Grant 1050747 and Millennium Science Nucleus “Complex Engineering Systems”, Chile and CNPq under PROSUL project Proc. 490333/2004-4, Brazil.

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