Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs

Authors:
Bruno Escoffier;Laurent Gourvès;Jérôme Monnot
Affiliations:
Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France and CNRS, FRE 3234, F-75775 Paris, France;CNRS, FRE 3234, F-75775 Paris, France and Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France;CNRS, FRE 3234, F-75775 Paris, France and Université de Paris-Dauphine, LAMSADE, F-75775 Paris, France
Venue:
Journal of Discrete Algorithms
Year:
2010

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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). Finally, dealing with hypergraphs, we study the complexity and the approximability of two natural generalizations.