Kernels in Cartesian products of digraphs

A kernel J of a digraph D is an independent set of vertices of D such that for every vertex w is an element of V(D) \ J there exists an arc from w to a vertex in J. In this paper we have obtained results for the existence and nonexistence of kernels in Cartesian products of certain families of digraphs, and characterized T square(C) over right arrow (n), T square(P) over right arrow (n) and (C) over right arrow (m)square(C) over right arrow (n) which have kernels, where T is a tournament, and (P) over right arrow (n) and (C) over right arrow (n) are, respectively, the directed path and the directed cycle of order n. Finally, we have introduced and studied kernel-partitionable digraphs.