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Algorithms for finding clique-transversals of graphs

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  • Guillermo Durán
  • Min Lin
  • Sergio Mera
  • Jayme Szwarcfiter

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

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:157:y:2008:i:1:p:37-45:10.1007/s10479-007-0189-x
    DOI: 10.1007/s10479-007-0189-x
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    References listed on IDEAS

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    1. 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, 2010. "Variations of maximum-clique transversal sets on graphs," Annals of Operations Research, Springer, vol. 181(1), pages 21-66, December.

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