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Cops and robbers in a random graph
- Source :
-
Journal of Combinatorial Theory - Series B . Mar2013, Vol. 103 Issue 2, p226-236. 11p. - Publication Year :
- 2013
-
Abstract
- Abstract: The cop-number of a graph is the minimum number of cops needed to catch a robber on the graph, where the cops and the robber alternate moving from a vertex to a neighbouring vertex. It is conjectured by Meyniel that for a graph on n vertices cops suffice. The aim of this paper is to investigate the cop-number of a random graph. We prove that for sparse random graphs the cop-number has order of magnitude . The best known strategy for general graphs is the area-defending strategy, where each cop ‘controls’ one region by himself. We show that, for general graphs, this strategy cannot be too effective: there are graphs that need at least cops for this strategy. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00958956
- Volume :
- 103
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 85405215
- Full Text :
- https://doi.org/10.1016/j.jctb.2012.10.002