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Covering graphs with few complete bipartite subgraphs.

Fleischner, H. and Mujuni, E. and Paulusma, Daniel and Szeider, S. (2009) 'Covering graphs with few complete bipartite subgraphs.', Theoretical computer science., 410 (21-23). pp. 2045-2053.

Abstract

We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique vertex-cover problem asks whether the vertex-set of the given graph can be covered with at most k bicliques, the biclique vertex-partition problem is defined similarly with the additional condition that the bicliques are required to be mutually vertex-disjoint. All these four problems are known to be NP-complete even if the given graph is bipartite. In this paper, we investigate them in the framework of parameterized complexity: do the problems become easier if k is assumed to be small? We show that, considering k as the parameter, the first two problems are fixed-parameter tractable, while the latter two problems are not fixed-parameter tractable unless P=NP.

Item Type:Article
Keywords:Bicliques, Parameterized complexity, Covering and partitioning problems.
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1016/j.tcs.2008.12.059
Record Created:14 Oct 2009 10:20
Last Modified:02 Apr 2013 16:53

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