FPT Algorithms for Domination in Biclique-Free Graphs

  • Jan Arne Telle
  • Yngve Villanger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

A class of graphs is said to be biclique-free if there is an integer t such that no graph in the class contains Kt,t as a subgraph. Large families of graph classes, such as any nowhere dense class of graphs or d-degenerate graphs, are biclique-free. We show that various domination problems are fixed-parameter tractable on biclique-free classes of graphs, when parameterizing by both solution size and t. In particular, the problems k-Dominating Set, Connected k-Dominating Set, Independent k-Dominating Set and Minimum Weight k-Dominating Set are shown to be FPT, when parameterized by t + k, on graphs not containing Kt,t as a subgraph. With the exception of Connected k-Dominating Set all described algorithms are trivially linear in the size of the input graph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jan Arne Telle
    • 1
  • Yngve Villanger
    • 1
  1. 1.Department of InformaticsUniversity of BergenNorway

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