A note on a Brooks' type theorem for DP-coloring
Abstract
Dvor\'ak and Postle DP introduced a 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 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 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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