  We consider a variant of the Cops and Robber game, in which the robber has
unbounded speed, i.e. can take any path from her vertex in her turn, but she is
not allowed to pass through a vertex occupied by a cop. Let c_{infty}(G) denote
the number of cops needed to capture the robber in a graph G in this variant.
We characterize graphs G with c_{infty}(G)=1, and give an O(|V(G)|^2) algorithm
for their detection. We prove a lower bound for c_{infty} of expander graphs,
and use it to prove three things. The first is that if np > 4.2 log n then the
random graph G = G(n,p) asymptotically almost surely has e1/p < c_{infty}(G) <
e2 log (np)/p, for suitable constants e1 and e2. The second is that a
fixed-degree random regular graph G with n vertices asymptotically almost
surely has c_{infty}(G) = Theta(n). The third is that if G is a Cartesian
product of m paths, then n / 4km^2 < c_{infty}(G) < n / k, where n=|V(G)| and k
is the number of vertices of the longest path.
