Variations of maximum-clique transversal sets on graphs

Chuan-Min Lee ()

Annals of Operations Research, 2010, vol. 181, issue 1, 66 pages

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

Keywords: Maximum-clique transversal function; Maximum-clique perfect; Signed maximum-clique transversal; Minus maximum-clique transversal; Hereditary clique-Helly graphs; Dually chordal graphs; Distance-hereditary graphs (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10479-009-0673-6

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