The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Graph Theory With Applications
Graph Theory With Applications
Eliminating graphs by means of parallel knock-out schemes
Discrete Applied Mathematics
Eliminating graphs by means of parallel knock-out schemes
Discrete Applied Mathematics
Upper bounds and algorithms for parallel knock-out numbers
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
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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 k rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time.