Bounds for the dichromatic number of a generalized lexicographic product of digraphs
Nopparat Pleanmani, Sayan Panma · Discrete Mathematics Algorithms and Applications · 2016
A subset [Formula: see text] is acyclic if it induces an acyclic subdigraph of a digraph [Formula: see text] and the dichromatic number [Formula: see text] of [Formula: see text] is defined to be the minimum integer [Formula: see text] such that [Formula: see text] can be partitioned into [Formula: see text] 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.