Domination When the Stars Are Out

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...

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Bibliographic Details
Published inAutomata, Languages and Programming pp. 462 - 473
Main Authors Hermelin, Danny, Mnich, Matthias, van Leeuwen, Erik Jan, Woeginger, Gerhard J.
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Free Graph
Graph Class
Interval Graph
Polynomial Kernel
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Summary: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 K1,4 as an induced subgraph. Our results provide a dichotomy for Dominating Set in K1,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.
ISBN:3642220053
9783642220050
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-22006-7_39