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 language | English |
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Pages (from-to) | 182-195 |
Number of pages | 14 |
Journal | Theoretical computer science |
Volume | 393 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - Mar 2008 |
Event | 7th Latin American Symposium on Theoretical Informatics, LATIN 2006 - Valdivia, Chile Duration: 20 Mar 2006 → 24 Mar 2006 Conference number: 7 |