The computational complexity of the parallel knock-out problem

Hajo Broersma, Matthew Johnson, Daniël Paulusma, Iain A. Stewart

    Research output: Contribution to journalArticleAcademicpeer-review

    5 Citations (Scopus)

    Abstract

    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 bipartite graph, such a scheme can be found that eliminates every vertex is NP-complete. Moreover, we show that, for all fixed positive integers $k\ge 2$, the problem of whether a given bipartite 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. We also show that $r$-regular graphs with $r\ge 1$, factor-critical graphs and 1-tough graphs admit a scheme in which all vertices are eliminated in one round.
    Original languageEnglish
    Pages (from-to)182-195
    Number of pages14
    JournalTheoretical computer science
    Volume393
    Issue number1-3
    DOIs
    Publication statusPublished - Mar 2008
    Event7th Latin American Symposium on Theoretical Informatics, LATIN 2006 - Valdivia, Chile
    Duration: 20 Mar 200624 Mar 2006
    Conference number: 7

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