  We generalize the graphical small cancellation theory of Gromov to a
graphical small cancellation theory over the free product. We extend Gromov's
small cancellation theorem to the free product. We explain and generalize
Rips-Segev's construction of torsion-free groups without the unique product
property by viewing these groups as given by graphical small cancellation
presentations over the free product. Our graphical small cancellation theorem
then provides first examples of Gromov hyperbolic groups without the unique
product property. We construct uncountably many non-isomorphic torsion-free
groups without the unique product property. We show that the presentations of
generalized Rips-Segev groups are not generic among finite presentations of
groups.
