Domination When the Stars Are Out

Details Domination When the Stars Are Out Domination When the Stars Are Out

2010-11-30

arxiv.org/abs/1012.0012v1

Computer Science

Data Structures and Algorithms

Scientific paper

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.

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