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)


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.


Polynomial Time Bipartite Graph Parameterized Complexity Computable Function Covering Graph 
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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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