Bounds for the dichromatic number of a generalized lexicographic product of digraphs

摘要

A subset U C V(D) is acyclic if it induces an acyclic subdigraph of a digraph D and the dichromatic number X_d(D) of D is defined to be the minimum integer n such that V(D) can be partitioned into n acyclic subsets. In this paper, we obtain lower and upper bounds for the dichromatic number of a generalized lexicographic product and the dichromatic number of a generalized corona of digraphs in terms of dichromatic numbers of those digraphs.