Defective DP-colorings of sparse simple graphs

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 simple graphs. Let \(g_{DP}(i,j,n)\) be the minimum number of edges in an \(n\)-vertex DP-\((i,j)\)-critical gr...

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Bibliographic Details
Published inarXiv.org
Main Authors Jing, Yifan, Kostochka, Alexandr, Ma, Fuhong, Xu, Jingwei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.06.2020
Subjects
Coloring
Graph theory
Graphs
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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 simple graphs. Let \(g_{DP}(i,j,n)\) be the minimum number of edges in an \(n\)-vertex DP-\((i,j)\)-critical graph. In this paper we determine sharp bound on \(g_{DP}(i,j,n)\) for each \(i\geq3\) and \(j\geq 2i+1\) for infinitely many \(n\).
ISSN:2331-8422