2 research outputs found
Meyniel's conjecture holds for random graphs
In the game of cops and robber, the cops try to capture a robber moving on
the vertices of the graph. The minimum number of cops required to win on a
given graph is called the cop number of . The biggest open conjecture in
this area is the one of Meyniel, which asserts that for some absolute constant
, the cop number of every connected graph is at most .
In this paper, we show that Meyniel's conjecture holds asymptotically almost
surely for the binomial random graph. We do this by first showing that the
conjecture holds for a general class of graphs with some specific
expansion-type properties. This will also be used in a separate paper on random
-regular graphs, where we show that the conjecture holds asymptotically
almost surely when .Comment: revised versio