Line graph

Multigraph

Philosophy

Complete coloring

Ecology

Biology

Discrete mathematics

Simple (philosophy)

Edge coloring

Brooks' theorem

Type (biology)

Graph

Mathematics

Epistemology

Mathematical analysis

List coloring

Fractional coloring

Combinatorics

Graph power

1-planar graph

Greedy coloring

Chordal graph

Generalization

Graph coloring

Journal of Graph Theory

Dvořák and Postle introduced DP‐coloring of simple graphs as a generalization of list‐coloring. They proved a Brooks' type theorem for DP‐coloring; and Bernshteyn, Kostochka, and Pron extended it to DP‐coloring of multigraphs. However, detailed structure, when a multigraph does not admit DP‐coloring, was not specified. 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.

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