Complexity and Approximation Results for the Connected Vertex Cover Problem in Graphs and Hypergraphs
Monnot, Jérôme; Gourvès, Laurent; Escoffier, Bruno (2010), Complexity and Approximation Results for the Connected Vertex Cover Problem in Graphs and Hypergraphs, Journal of Discrete Algorithms, 8, 1, p. 36-49. http://dx.doi.org/10.1016/j.jda.2009.01.005
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00178912/en/
Journal nameJournal of Discrete Algorithms
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Abstract (EN)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.
Subjects / KeywordsConnected vertex cover; Chordal graphs; Bipartite graphs; Planar graphs; Hypergraphs; Approximation algorithm
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