The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Bipartite graphs and their applications
Bipartite graphs and their applications
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
Upper bounds and algorithms for parallel knock-out numbers
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Upper bounds and algorithms for parallel knock-out numbers
Theoretical Computer Science
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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 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=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=1, factor-critical graphs and 1-tough graphs admit a scheme in which all vertices are eliminated in one round.