A sufficient condition for kernel perfectness of a digraph in terms of semikernels modulo F

A kernel of a directed graph is a set of vertices which is both independent and absorbent. And a digraph is said to be kernel perfect if and only if any induced subdigraph has a kernel. Given a set of arcs F , a semikernel S modulo F is an independent set such that if some Sz-arc is not in F , then there exists a zS-arc. A sufficient condition on the digraph is given in terms of semikernel modulo F in order to guarantee that a digraph is kernel perfect. To do that first we give a characterization of kernel perfectness which is a generalization of a previous result given by V. Neumann-Lara [Seminúcleos de una digráfica. Anales del Instituto de Matemáticas 2, Universidad Nacional Autónoma de México (1971)]. And moreover, we show by means of an example that our result is not a consequence of previous known sufficient conditions.