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Friday 08 April 2011, 14:00-15:00
Domination When the Stars Are Out – An algorithmization of Chudnovsky’s and Seymour’s Structure Theorem for Claw-Free Graphs
- 👤 Speaker: Matthias Mnich, International Computer Science Institute, Berkeley
- 📅 Date & Time: Friday 08 April 2011, 14:00 - 15:00
- 📍 Venue: Room FW11, Computer Laboratory, William Gates Building
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.
(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)
Series This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.
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