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Algorithms for finding clique-transversals of graphs. (English) Zbl 1163.90768
Summary: 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 $$\tau_c$$ 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 $$\tau_c$$. 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 $$\tau_c$$ 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.

##### MSC:
 90C35 Programming involving graphs or networks
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##### References:
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