Defective DP-colorings of sparse multigraphs

DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle. We introduce and study (i,j)-defective DP-colorings of multigraphs. We concentrate on sparse multigraphs and consider fDP(i,j,n) — the minimum number of edges that may ha...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 93; p. 103267
Main Authors Jing, Yifan, Kostochka, Alexandr, Ma, Fuhong, Sittitrai, Pongpat, Xu, Jingwei
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2021
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Summary:DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle. We introduce and study (i,j)-defective DP-colorings of multigraphs. We concentrate on sparse multigraphs and consider fDP(i,j,n) — the minimum number of edges that may have an n-vertex (i,j)-critical multigraph, that is, a multigraph G that has no (i,j)-defective DP-coloring but whose every proper subgraph has such a coloring. For every i and j, we find linear lower bounds on fDP(i,j,n) that are exact for infinitely many n.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2020.103267