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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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