Complexity and approximation results for the connected vertex cover problem

Authors:
Bruno Escoffier;Laurent Gourvès;Jérôme Monnot
Affiliations:
CNRS, LAMSADE, Université Paris-Dauphine, Tassigny, Paris Cedex 16, France;CNRS, LAMSADE, Université Paris-Dauphine, Tassigny, Paris Cedex 16, France;CNRS, LAMSADE, Université Paris-Dauphine, Tassigny, Paris Cedex 16, France
Venue:
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Year:
2007

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Abstract

We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APX-hard in bipartite graphs and is 5/3-approximable in any class of graphs where the vertex cover problem is polynomial (in particular in bipartite graphs).