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Complexity and algorithms for the connected vertex cover problem in 4-regular graphs

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  • Li, Yuchao
  • Yang, Zishen
  • Wang, Wei

Abstract

In the connected vertex cover (CVC) problem, we are given a connected graph G and required to find a vertex cover set C with minimum cardinality such that the induced subgraph G[C] is connected. In this paper, we restrict our attention to the CVC problem in 4-regular graphs. We proved that the CVC problem is still NP-hard for 4-regular graphs and gave a lower bound for the problem. Moreover, we proposed two approximation algorithms for CVC problem with approximation ratio 32 and 43+O(1n), respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:301:y:2017:i:c:p:107-114
    DOI: 10.1016/j.amc.2016.12.004
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    Cited by:

    1. Brešar, Boštjan & Kos, Tim & Krivoš-Belluš, Rastislav & Semanišin, Gabriel, 2019. "Hitting subgraphs in P4-tidy graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 211-219.
    2. 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.
    3. Boris Brimkov & Derek Mikesell & Logan Smith, 2019. "Connected power domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 292-315, July.
    4. Gusev, Vasily V., 2023. "Set-weighted games and their application to the cover problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 438-450.
    5. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.

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