  We consider a variant of the Cops and Robber game, introduced by Fomin,
Golovach, Kratochvil, 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. We study this game on interval graphs, chordal
graphs, planar graphs, and hypercube graphs. Let c_{\infty}(G) denote the
number of cops needed to capture the robber in graph G in this variant. We show
that if G is an interval graph, then c_{\infty}(G) = O(sqrt(|V(G)|)), and we
give a polynomial-time 3-approximation algorithm for finding c_{\infty}(G) in
interval graphs. We prove that for every n there exists an n-vertex chordal
graph G with c_{\infty}(G) = Omega(n / \log n). Let tw(G) and Delta(G) denote
the treewidth and the maximum degree of G, respectively. We prove that for
every G, tw(G) + 1 \leq (Delta(G) + 1) c_{\infty}(G). Using this lower bound
for c_{\infty}(G), we show two things. The first is that if G is a planar graph
(or more generally, if G does not have a fixed apex graph as a minor), then
c_{\infty}(G) = Theta(tw(G)). This immediately leads to an O(1)-approximation
algorithm for computing c_{\infty} for planar graphs. The second is that if G
is the m-hypercube graph, then there exist constants eta1, eta2>0 such that
(eta1) 2^m / (m sqrt(m)) \leq c_{\infty}(G) \leq (eta2) 2^m / m.
