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Domination When the Stars Are Out

  • Danny Hermelin
  • Matthias Mnich
  • Erik Jan van Leeuwen
  • Gerhard J. Woeginger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K 1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K 1,ℓ-free graphs and show that the problem is fixed-parameter tractable if and only if ℓ ≤ 3. Finally, we show that our algorithmization can also be used to show that the related Connected Dominating Set problem is fixed-parameter tractable on claw-free graphs.

Keywords

Vertex Cover Interval Graph Polynomial Kernel Graph Class Free 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 2011

Authors and Affiliations

  • Danny Hermelin
    • 1
  • Matthias Mnich
    • 2
  • Erik Jan van Leeuwen
    • 3
  • Gerhard J. Woeginger
    • 4
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.International Computer Science InstituteBerkeleyUSA
  3. 3.Department of InformaticsUniversity of BergenNorway
  4. 4.Department of Mathematics and Computer ScienceTU EindhovenThe Netherlands

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