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Connected vertex cover for (sP1+P5)-free graphs.

Johnson, M. and Paesani, G. and Paulusma, D. (2020) 'Connected vertex cover for (sP1+P5)-free graphs.', Algorithmica., 82 (1). pp. 20-40.

Abstract

The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most k that induces a connected subgraph of G. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in particular, for H-free graphs if H is not a linear forest. On the other hand, the problem is known to be polynomial-time solvable for s P2-free graphs for any integer s ≥ 1. We give a polynomial-time algorithm to solve the problem for (s P1 + P5)-free graphs for every integer s ≥ 0. Our algorithm can also be used for the Weighted Connected Vertex Cover problem.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00453-019-00601-9
Publisher statement:This is a post-peer-review, pre-copyedit version of an article published in Algorithmica. The final authenticated version is available online at: https://doi.org/10.1007/s00453-019-00601-9
Date accepted:12 June 2019
Date deposited:13 June 2019
Date of first online publication:20 June 2019
Date first made open access:20 June 2020

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