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The connected vertex cover problem in k-regular graphs

Author

Listed:
  • Yuchao Li

    (Xi’an Jiaotong University)

  • Wei Wang

    (Xi’an Jiaotong University)

  • Zishen Yang

    (Xi’an Jiaotong University)

Abstract

Given a connected graph $$G=(V,E)$$ G = ( V , E ) , the Connected Vertex Cover (CVC) problem is to find a vertex set $$S\subset V$$ S ⊂ V with minimum cardinality such that every edge is incident to a vertex in S, and moreover, the induced graph G[S] is connected. In this paper, we investigate the CVC problem in k-regular graphs for any fixed k ( $$k\ge 4$$ k ≥ 4 ). First, we prove that the CVC problem is NP-hard for k-regular graphs,and then we give a lower bound for the minimum size of a CVC, based on which, we propose a $$\frac{2k}{k+2}+O(\frac{1}{n})$$ 2 k k + 2 + O ( 1 n ) -approximation algorithm for the CVC problem.

Suggested Citation

  • Yuchao Li & Wei Wang & Zishen Yang, 2019. "The connected vertex cover problem in k-regular graphs," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 635-645, August.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:2:d:10.1007_s10878-019-00403-3
    DOI: 10.1007/s10878-019-00403-3
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    References listed on IDEAS

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    1. Li, Yuchao & Yang, Zishen & Wang, Wei, 2017. "Complexity and algorithms for the connected vertex cover problem in 4-regular graphs," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 107-114.
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    Cited by:

    1. Zishen Yang & Wei Wang & Majun Shi, 2021. "Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 673-695, March.

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