  The Erdos-Hajnal conjecture says that for every graph H there exists c>0 such
that every graph G not containing H as an induced subgraph has a clique or
stable set of cardinality at least |G|^c. We prove that this is true when H is
a cycle of length five.
  We also prove several further results: for instance, that if C is a cycle and
H is the complement of a forest, there exists c>0 such that every graph G
containing neither of C,H as an induced subgraph has a clique or stable set of
cardinality at least |G|^c.
