Domination when the stars are out

D. Hermelin, M. Mnich, E.J. Leeuwen, van, G.J. Woeginger

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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 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
Original languageEnglish
Number of pages49
Publication statusPublished - 2010

Publication series [cs.DS]


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