Bruno Escoffier, Laurent Gourvès, Jérôme Monnot. Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs. 2007. hal-00178912  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.
Escoffier, Gourvès, and Monnot REF improved the latter result by showing that Connected Vertex Cover is polynomial-time solvable for chordal graphs.
Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs
J. Discrete Algorithms
J. Discrete Algorithms
Mathematics Computer Science