  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.
