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2008

The computational complexity of the parallel knock-out problem

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The computational complexity of the parallel knock-out problem
We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for a given graph, such a scheme can be found that eliminates every vertex is NP-complete. Moreover, we show that, for all fixed positive integers k 2, the problem of whether a given graph admits a scheme in which all vertices are eliminated in at most (exactly) k rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time.
Hajo Broersma, Matthew Johnson 0002, Daniël P
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Hajo Broersma, Matthew Johnson 0002, Daniël Paulusma, Iain A. Stewart
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