Abstract
Given a connected graph \(G=(V,E)\), the Connected Vertex Cover (CVC) problem is to find a vertex set \(S\subset V\) 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 (\(k\ge 4\)). 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 \(\frac{2k}{k+2}+O(\frac{1}{n})\)-approximation algorithm for the CVC problem.
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The funding was provided by National Natural Science Foundation of China (11471005).
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Li, Y., Wang, W. & Yang, Z. The connected vertex cover problem in k-regular graphs. J Comb Optim 38, 635–645 (2019). https://doi.org/10.1007/s10878-019-00403-3
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DOI: https://doi.org/10.1007/s10878-019-00403-3