Even directed cycles in H-free digraphs

A digraph is H-free if its underlying graph does not contain a subgraph contractible to the graph H. We provide a polynomial-time algorithm to solve the even cycle problem in the class of K-3,K-3-free digraphs and in the class of K-5-free digraphs. We also discuss the important role played bg the subdivisions of K-3,K-3 in solving the even cycle problem in its generality.