2011 | OriginalPaper | Buchkapitel
Domination When the Stars Are Out
verfasst von : Danny Hermelin, Matthias Mnich, Erik Jan van Leeuwen, Gerhard J. Woeginger
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
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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.