On DP-coloring of digraphs

DP-coloring is a relatively new coloring concept by Dvorak and Postle and was introduced as an extension of list-colorings of (undirected) graphs. It transforms the problem of finding a list-coloring of a given graph G with a list-assignment L to finding an independent transversal in an auxiliary graph with vertex set {(v,c)|v is an element of V(G),c is an element of L(v)}. In this paper, we extend the definition of DP-colorings to digraphs using the approach from Neumann-Lara where a coloring of a digraph is a coloring of the vertices such that the digraph does not contain any monochromatic directed cycle. Furthermore, we prove a Brooks' type theorem regarding the DP-chromatic number, which extends various results on the (list-)chromatic number of digraphs.