Some results on the structure of kernel-perfect and critical kernel-imperfect digraphs

A kernel N of a digraph D is an independent set of vertices of D such that for every w ∈ V (D) − N there exists an arc from w to N . The digraph D is said to be a kernel-perfect digraph when every induced subdigraph of D has a kernel. Minimal non kernel-perfect digraphs are called critical kernel imperfect digraphs. In this paper some new structural results concerning finite critical kernel imperfect digraphs are presented. Also we present new sufficient conditions for a finite or infinite digraph to have a kernel.