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

Author

Listed:
  • Ke Liu

    (Tsinghua University)

  • Mei Lu

    (Tsinghua University)

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.

Suggested Citation

  • Ke Liu & Mei Lu, 2021. "Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 923-933, May.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:4:d:10.1007_s10878-021-00703-7
    DOI: 10.1007/s10878-021-00703-7
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    References listed on IDEAS

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    1. Guillermo Durán & Min Lin & Jayme Szwarcfiter, 2002. "On Clique-Transversals and Clique-Independent Sets," Annals of Operations Research, Springer, vol. 116(1), pages 71-77, October.
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    Cited by:

    1. Chuan-Min Lee, 2023. "Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective," Mathematics, MDPI, vol. 11(15), pages 1-33, July.

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