A theorem about a conjecture of H. Meyniel on kernel-perfect graphs

Abstract A diagraph D is said to be an R -digraph (kernel-perfect graph) if all of its induced subdigraphs possesses a kernel (independent dominating subset). I show in this work that a digraph D , without directed triangles all of whose odd directed cycles C = (1,2,…,2 n + 1, 1), possesses two short chords (that means there exist two arcs of D of the form: ( q , q +2) and ( q ′, q ′ + 2)) is an R -digraph.