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

Galeana-Sanchez, H., On the existence of kernels and h-kernels in directed graphs, Discrete Mathematics 110 (1992) 2.51-255. A directed graph D with vertex set V is called cyclically h-partite (h > 2) provided one can partition V = V, + V, +. . + V,_, so that if (u, u) is an arc of D then u E V,, and u E v+, (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.