Domination when the stars are out

D. Hermelin, M. Mnich, E.J. Leeuwen, van, G.J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

18 Citations (Scopus)
1 Downloads (Pure)

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.
Original languageEnglish
Title of host publicationAutomata, Languages and Programming (38th International Colloquium, ICALP 2011, Zürich, Switzerland, July 4-8, 2011. Proceedings, Part I)
EditorsL. Aceto, M. Henzinger, J. Sgall
Place of PublicationBerlin
PublisherSpringer
Pages462-473
ISBN (Print)978-3-642-22005-0
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Computer Science
Volume6755
ISSN (Print)0302-9743

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