On the existence of kernels and h-kernels in directed graphs

AbstractA directed graph D with vertex set V is called cyclically h-partite (h⩾2) provided one can partition V=V0+V1+⋯+Vh−1 so that if (u, υ) is an arc of D then uϵVi, and υϵVi+1 (notation mod h). In this communication we obtain a characterization of cyclically h-partite strongly connected digraphs. As a consequence we obtain a sufficient condition for a digraph to have a h-kernel