  A graph is path-pairable if for any pairing of its vertices there exist edge
disjoint paths joining the vertices in each pair. We obtain sharp bounds on the
maximum possible diameter of path-pairable graphs which either have a given
number of edges, or are c- degenerate. Along the way we show that a large
family of graphs obtained by blowing up a path is path-pairable, which may be
of independent interest.
