Algorithms for finding clique-transversals of graphs

Guillermo Durán (), Min Lin (), Sergio Mera () and Jayme Szwarcfiter ()

Annals of Operations Research, 2008, vol. 157, issue 1, 37-45

Abstract: A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ c . This algorithm is employed for finding the minimum cardinality clique-transversal of $\overline{3K_{2}}$ -free circular-arc graphs in O(n 4 ) time. Further we describe an algorithm for determining τ c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n 2 ) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n 2 ) time. Copyright Springer Science+Business Media, LLC 2008

Keywords: Algorithms; Circular-arc graphs; Clique-transversals; Helly circular-arc graphs; $\overline{3K_{2}}$ -free circular-arc graphs (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10479-007-0189-x

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