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arXiv · 1812.09684

On DP-Coloring of Digraphs

Jørgen Bang-Jensen·Thomas Bellitto·Thomas Schweser·Michael Stiebitz
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Abstract

DP-coloring is a relatively new coloring concept by Dvo\v{r}\'ak 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 $\{(v,c) ~|~ v \in V(G), c \in L(v)\}$. 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.

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Jørgen Bang-Jensen, Thomas Bellitto, Thomas Schweser, Michael Stiebitz. 2018-12-23. On DP-Coloring of Digraphs. https://arxiv.org/abs/1812.09684

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