The connected vertex cover problem in k-regular graphs

Yuchao Li (), Wei Wang () and Zishen Yang ()
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Yuchao Li: Xi’an Jiaotong University
Wei Wang: Xi’an Jiaotong University
Zishen Yang: Xi’an Jiaotong University

Journal of Combinatorial Optimization, 2019, vol. 38, issue 2, No 17, 635-645

Abstract: 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.

Keywords: Connected vertex cover problem; Approximation algorithm; k-Regular graph; 05C85; 05C70 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-019-00403-3

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