  We consider a game in which a cop searches for a moving robber on a graph
using distance probes, which is a slight variation on one introduced by Seager.
Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph
$G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by
replacing each edge of $G$ by a path of length $m$, if $m \geqslant n$. They
conjectured that this bound was best possible for complete graphs, but the
present authors showed that in fact the cop wins on $K^{1/m}$ if and only if $m
\geqslant n/2$, for all but a few small values of $n$. In this paper we extend
this result to general graphs by proving that the cop has a winning strategy on
$G^{1/m}$ provided $m \geqslant n/2$ for all but a few small values of $n$;
this bound is best possible. We also consider replacing the edges of $G$ with
paths of varying lengths.
