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

Ke Liu () and Mei Lu ()
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Ke Liu: Tsinghua University
Mei Lu: Tsinghua University

Journal of Combinatorial Optimization, 2021, vol. 41, issue 4, No 9, 923-933

Abstract: Abstract Let $$G=(V,E)$$ 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 $$\Phi _C(G)$$ Φ C ( G ) be the set of all complete subgraphs of G and $$\Phi \subseteq {\Phi }_C(G)$$ Φ ⊆ Φ C ( G ) . In this paper, we consider the Complete-Subgraph-Transversal-Set on $$\Phi $$ Φ problem and the L-Max Complete-Subgraph-Transversal-Set on $$\Phi $$ Φ 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.

Keywords: Treewidth; Complete subgraph; NP-complete problems; Algorithms (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-021-00703-7

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