Algorithms for finding clique-transversals of graphs |
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Authors: | Guillermo Durán Min Chih Lin Sergio Mera Jayme L. Szwarcfiter |
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Affiliation: | (1) Departamento de Ingeniería Industrial, Universidad de Chile, Santiago, Chile;(2) Departamento de Computación, Universidad de Buenos Aires, Buenos Aires, Argentina;(3) Universidade Federal do Rio de Janeiro, I. Matemática, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brasil |
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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 [`(3K2)]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. |
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Keywords: | Algorithms Circular-arc graphs Clique-transversals Helly circular-arc graphs IEq2" > /content/kp21325n80217x5w/10479_2007_189_Article_IEq2.gif" alt=" $overline{3K_{2}}$" align=" middle" border=" 0" > -free circular-arc graphs |
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