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Variations of maximum-clique transversal sets on graphs

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  • Chuan-Min Lee

Abstract

A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we introduce the concept of maximum-clique perfect and some variations of the maximum-clique transversal set problem such as the {k}-maximum-clique, k-fold maximum-clique, signed maximum-clique, and minus maximum-clique transversal problems. We show that balanced graphs, strongly chordal graphs, and distance-hereditary graphs are maximum-clique perfect. Besides, we present a unified approach to these four problems on strongly chordal graphs and give complexity results for the following classes of graphs: split graphs, balanced graphs, comparability graphs, distance-hereditary graphs, dually chordal graphs, doubly chordal graphs, chordal graphs, planar graphs, and triangle-free graphs. Copyright Springer Science+Business Media, LLC 2010

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  • Chuan-Min Lee, 2010. "Variations of maximum-clique transversal sets on graphs," Annals of Operations Research, Springer, vol. 181(1), pages 21-66, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:21-66:10.1007/s10479-009-0673-6
    DOI: 10.1007/s10479-009-0673-6
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    References listed on IDEAS

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    1. Guillermo Durán & Min Lin & Sergio Mera & Jayme Szwarcfiter, 2008. "Algorithms for finding clique-transversals of graphs," Annals of Operations Research, Springer, vol. 157(1), pages 37-45, January.
    2. Guillermo Durán & Min Lin & Jayme Szwarcfiter, 2002. "On Clique-Transversals and Clique-Independent Sets," Annals of Operations Research, Springer, vol. 116(1), pages 71-77, October.
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    Cited by:

    1. Chuan-Min Lee, 2023. "Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective," Mathematics, MDPI, vol. 11(15), pages 1-33, July.

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