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Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs

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Abstract

Let \(G=(V,E)\) be a graph. A complete subgraph of G is a subgraph of pairwise adjacent vertices of V of size at least 2. Let \(\Phi _C(G)\) be the set of all complete subgraphs of G and \(\Phi \subseteq {\Phi }_C(G)\). In this paper, we consider the Complete-Subgraph-Transversal-Set on \(\Phi \) problem and the L-Max Complete-Subgraph-Transversal-Set on \(\Phi \) problem. We give polynomial time algorithms to these two problems on graphs of bounded treewidth. At last, we show the connections between these two problems with some other NP-complete problems, for example Clique-Transversal-Set problem on graphs and Vertex-Cover problem on hypergraphs.

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Acknowledgements

Many thanks to the anonymous referee for his/her many helpful comments and suggestions, which have considerably improved the presentation of the paper. This work is partially supported by the National Natural Science Foundation of China (Grants 11771247 and 11971158) and Tsinghua University Initiative Scientific Research Program.

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  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Ke Liu & Mei Lu

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  1. Ke Liu
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  2. Mei Lu
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Correspondence to Mei Lu.

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Liu, K., Lu, M. Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs. J Comb Optim 41, 923–933 (2021). https://doi.org/10.1007/s10878-021-00703-7

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