A Richardson's theorem version for Î -kernels

In this paper we prove the following result: Let D be a digraph and Π⊆DP(D). If there is a partition P={Πi}i∈I of Π such that: For each i∈I, Πi is transitive; and CD(P) has no odd cycles of order greater than 1, then D has Π- kernel. Some interesting previous results are obtained as a direct consequence of this result.