Cops and robbers in a random graph

Authors:
BéLa BollobáS;GáBor Kun;Imre Leader
Affiliations:
Trinity College, Cambridge CB2 1TQ, UK;School of Computing Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;Trinity College, Cambridge CB2 1TQ, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

Citing 7
Cited 0

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Cops and robbers in graphs with large girth and Cayley graphs

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A better bound for the cop number of general graphs

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Chasing robbers on random graphs: Zigzag theorem

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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 O(n) 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 n^1^/^2^+^o^(^1^). 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 n^1^-^o^(^1^) cops for this strategy.