  We study a generalization of the well-known disjoint paths problem which we
call the metric Menger problem, denoted MM(r,k), where one is given two subsets
of a graph and must decide whether they can be connected by $k$ paths of
pairwise distance at least $r$. We prove that this problem is NP-complete for
every $r\geq 3$ and $k\geq 2$ by giving a reduction from 3SAT. This resolves a
conjecture recently stated by Georgakopoulos and Papasoglu. On the other hand,
we show that the problem is in XP when parameterised by treewidth and maximum
degree by observing that it is `locally checkable'. In the case $r\leq 3$, we
prove that it suffices to parameterise by treewidth. We also state some open
questions relating to this work.
