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doi:10.1016/j.dam.2007.05.048 
Copyright © 2007 Elsevier B.V. All rights reserved.
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Flavia Bonomoa, 1, 
, Maria Chudnovskyb, c, 2, and Guillermo Duránd, 3,
Received 27 June 2005;
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.
Keywords: Claw-free graphs; Clique-perfect graphs; Hereditary clique-Helly graphs; Line graphs; Perfect graphs
Article Outline
- 1. Introduction
- 2. Preliminaries
- 3. Partial characterizations
- 3.1. Line graphs
- 3.2. HCH claw-free graphs
- 3.2.1. Circular interval graphs
- 3.2.2. Decompositions
- 3.2.3. Basic classes
- 3.2.4. Proof of Theorem 19
- 4. Summary
- Acknowledgements
- References
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An extended abstract of this paper was presented at GRACO 2005 (second Brazilian Symposium on Graphs, Algorithms, and Combinatorics) and appeared, under a different title, in Electronic Notes in Discrete Mathematics 19 (2005) 95–101.
1 Partially supported by UBACyT Grant X184, PICT ANPCyT Grant 11-09112, Argentina, and CNPq under PROSUL Project Proc. 490333/2004-4, Brazil.
2 This research was conducted during the period the author served as a Clay Mathematics Institute Research Fellow. The research was conducted in part at Princeton University.
3 Partially supported by FONDECyT Grant 1050747, Millennium Science Nucleus “Complex Engineering Systems”, Chile, and CNPq under PROSUL Project Proc. 490333/2004-4, Brazil.
