Algorithms for finding clique-transversals of graphs
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 t...
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| Autores principales: | , , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02545330_v157_n1_p37_Duran |
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| Sumario: | 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 3K2̄-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. © 2007 Springer Science+Business Media, LLC. |
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