Cops and robbers in random graphs
Combinatorics
2008-05-20 v1
Abstract
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.
Cite
@article{arxiv.0805.2709,
title = {Cops and robbers in random graphs},
author = {Bela Bollobas and Gabor Kun and Imre Leader},
journal= {arXiv preprint arXiv:0805.2709},
year = {2008}
}
Comments
15 pages. J. Comb. Theory B, submitted