Covering Graphs with Few Complete Bipartite Subgraphs
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
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.
Description
Ful text can be accessed at
http://www.sciencedirect.com/science/article/pii/S0304397508009407
Keywords
Bicliques, Parameterized complexity, Covering and partitioning problems
Citation
Fleischner, H., Mujuni, E., Paulusma, D. and Szeider, S., 2009. Covering graphs with few complete bipartite subgraphs. Theoretical Computer Science, 410(21), pp.2045-2053.