We show that a group that is hyperbolic relative to strongly shortcut groups
is itself strongly shortcut, thus obtaining new examples of strongly shortcut
groups. The proof relies on a result of independent interest: we show that
every relatively hyperbolic group acts properly and cocompactly on a graph in
which the parabolic subgroups act properly and cocompactly on convex subgraphs.Comment: 13 pages, 6 figures. v2: Improved introductio