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Official URL: http://dx.doi.org/10.1016/j.tcs.2007.11.021

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 , the problem of whether a given bipartite graph admits a scheme in which all vertices are eliminated in at most (exactly) 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 -regular graphs with , factor-critical graphs and 1-tough graphs admit a scheme in which all vertices are eliminated in one round.

Available Versions of this Item

• The Computational Complexity of the Parallel Knock-Out Problem (deposited 21 December 2006)
  • The computational complexity of the parallel knock-out problem (deposited 15 December 2008)
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