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arXiv · 1709.09807

A note on a Brooks' type theorem for DP-coloring

Seog-Jin Kim·Kenta Ozeki
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Abstract

Dvořák and Postle \cite{DP} introduced a \textit{DP-coloring} of a simple graph as a generalization of a list-coloring. They proved a Brooks' type theorem for a DP-coloring, and Bernshteyn, Kostochka and Pron \cite{BKP} extended it to a DP-coloring of multigraphs. However, detailed structure when a multigraph does not admit a DP-coloring was not specified in \cite{BKP}. In this note, we make this point clear and give the complete structure. This is also motivated by the relation to signed coloring of signed graphs.

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Seog-Jin Kim, Kenta Ozeki. 2017-09-28. A note on a Brooks' type theorem for DP-coloring. https://arxiv.org/abs/1709.09807

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