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.

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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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