%0 Journal Article
%T Cops and robbers in random graphs
%A Bela Bollobas
%A Gabor Kun
%A Imre Leader
%J Mathematics
%D 2008
%I arXiv
%X We consider the pursuit and evasion game on finite, connected, undirected graphs known as cops and robbers. Meyniel conjectured that for every graph on n vertices a rootish number of cops can win the game. We prove that this holds up to a log(n) factor for random graphs G(n,p) if p is not very small, and this is close to be tight unless the graph is very dense. We analyze the area-defending strategy (used by Aigner in case of planar graphs) and show examples where it can not be too efficient.
%U http://arxiv.org/abs/0805.2709v1