  We show that if H is a quasiconvex subgroup of a hyperbolic group G then the
relative Cayley graph Y (also known as the Schreier coset graph) for G/H is
Gromov-hyperbolic. We also observe that in this situation if G is torsion-free
and non-elementary and H has infinite index in G then the simple random walk on
Y is transient.
