On the disc-structure of perfect graphs II. The co-C4-structure O

Let F be any family of graphs. Two graphs G1=(V1,E1),G2=(V2,E2) are said to have the same F-structure if there is a bijection f : V1→V2 such that a subset S induces a graph belonging to F in G1 iff its image f(S) induces a graph belonging to F in G2. We prove that if a C5-free graph H has the {2K2,C4}-structure of a perfect graph G then H is perfect.