University of Cambridge > Talks.cam > Logic and Semantics Seminar (Computer Laboratory) > Domination When the Stars Are Out – An algorithmization of Chudnovsky’s and Seymour’s Structure Theorem for Claw-Free Graphs

Domination When the Stars Are Out – An algorithmization of Chudnovsky’s and Seymour’s Structure Theorem for Claw-Free Graphs

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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.

(joint work with Danny Hermelin, Erik Jan van Leeuwen and Gerhard Woeginger – Max Planck Institut fur Informatik, University of Bergen/Norway, and TU Eindhoven/Netherlands)

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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