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 language | English |
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Publisher | s.n. |
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Number of pages | 49 |
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Publication status | Published - 2010 |
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Name | arXiv.org [cs.DS] |
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Volume | 1012.0012 |
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