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Covering Graphs with Few Complete Bipartite Subgraphs

  • Herbert Fleischner
  • Egbert Mujuni
  • Daniel Paulusma
  • Stefan Szeider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4855)

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.

Keywords

Polynomial Time Bipartite Graph Parameterized Complexity Computable Function Covering Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Herbert Fleischner
    • 1
  • Egbert Mujuni
    • 2
  • Daniel Paulusma
    • 3
  • Stefan Szeider
    • 3
  1. 1.Department of Computer Science, Vienna Technical University, A-1040 ViennaAustria
  2. 2.Mathematics Department, University of Dar es Salaam, PO Box 35062, Dar es SalaamTanzania
  3. 3.Department of Computer Science, Durham University, Durham DH1 3LEUnited Kingdom

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