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

Bruno Escoffier (1) , Laurent Gourvès (1) , Jérôme Monnot (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

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.

Mots clés: approximation algorithm; Connected vertex cover; chordal graphs; bipartite graphs; planar graphs; hypergraphs; APX-complete; approximation algorithm.

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Bruno Escoffier, Laurent Gourvès, Jérôme Monnot. Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs. 2007. ⟨hal-00178912⟩