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Knocking out P_k-free graphs.

Johnson, M. and Paulusma, D. and Stewart, A. (2014) 'Knocking out P_k-free graphs.', in 39th International Symposium, MFCS 2014, Budapest, Hungary, 26-29August 2014 ; proceedings, Part II. Berlin, Heidelberg: Springer, pp. 396-407. Lecture notes in computer science. (8635).


A parallel knock-out scheme for a graph proceeds in rounds in each of which each surviving vertex eliminates one of its surviving neighbours. A graph is KO-reducible if there exists such a scheme that eliminates every vertex in the graph. The Parallel Knock-Out problem is to decide whether a graph G is KO-reducible. This problem is known to be NP-complete and has been studied for several graph classes since MFCS 2004. We show that the problem is NP-complete even for split graphs, a subclass of P 5-free graphs. In contrast, our main result is that it is linear-time solvable for P 4-free graphs (cographs).

Item Type:Book chapter
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Date accepted:No date available
Date deposited:15 January 2015
Date of first online publication:2014
Date first made open access:No date available

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