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The computational complexity of the parallel knock-out problem.

Broersma, Hajo and Johnson, Matthew and Paulusma, Daniel and Stewart, Iain A. (2006) 'The computational complexity of the parallel knock-out problem.', in LATIN 2006 : theoretical informatics: : 7th Latin American symposium, Valdivia, Chile, March 20-24, 2006 : proceedings. Berlin: Springer, pp. 250-261. Lecture notes in computer science. (3887).


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 <i>k</i> > 1, the problem of whether a given graph admits a scheme in which all vertices are eliminated in at most <i>k</i> rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time.

Item Type:Book chapter
Keywords:Parallel knock-out, Graphs, Computational complexity.
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:11 December 2015
Date of first online publication:February 2006
Date first made open access:No date available

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