Covering graphs with few complete bipartite subgraphs

Authors:
Herbert Fleischner;Egbert Mujuni;Daniel Paulusma;Stefan Szeider
Affiliations:
Department of Computer Science, Vienna Technical University, Vienna, Austria;Mathematics Department, University of Dar es Salaam, Dar es Salaam, Tanzania;Department of Computer Science, Durham University, Durham, United Kingdom;Department of Computer Science, Durham University, Durham, United Kingdom
Venue:
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Year:
2007

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Abstract

Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the given graph can be covered with at most k bicliques (complete bipartite subgraphs); the biclique vertex-cover problem asks whether the vertex-set of the given graph can be covered with at most k bicliques. Both problems are known to be NP-complete even if the given graph is bipartite. In this paper we investigate these two problems 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 problem is fixed-parameter tractable, while the second one is not fixed-parameter tractable unless P = NP.