A note on a Brooks' type theorem for DP-coloring |
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| Authors: | Seog-Jin Kim Kenta Ozeki |
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| Institution: | 1. Department of Mathematics Education, Konkuk University, Seoul, Korea;2. Faculty of Environment and Information Sciences, Yokohama National University, Yokohama, Japan |
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| Abstract: | 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. |
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| Keywords: | Brooks' type theorem coloring DP-coloring list-coloring |
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