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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| Published in | European journal of combinatorics Vol. 93; p. 103267 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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01.03.2021
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 103267 |
| Author | Kostochka, Alexandr Ma, Fuhong Sittitrai, Pongpat Xu, Jingwei Jing, Yifan |
| Author_xml | – sequence: 1 givenname: Yifan surname: Jing fullname: Jing, Yifan email: yifanj6@illinois.edu organization: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA – sequence: 2 givenname: Alexandr surname: Kostochka fullname: Kostochka, Alexandr email: kostochk@math.uiuc.edu organization: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA – sequence: 3 givenname: Fuhong surname: Ma fullname: Ma, Fuhong email: fma@ustc.edu.cn organization: School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China – sequence: 4 givenname: Pongpat surname: Sittitrai fullname: Sittitrai, Pongpat email: pongpat_s@kkumail.com organization: Department of Mathematics, Faculty of Science, Khon Kaen University, 40002, Thailand – sequence: 5 givenname: Jingwei surname: Xu fullname: Xu, Jingwei email: jx6@illinois.edu organization: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA |
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| Cites_doi | 10.1002/jgt.3190110408 10.1007/s00493-018-3733-1 10.1016/j.dam.2011.06.021 10.7151/dmgt.1557 10.1002/jgt.3190100207 10.1017/S0963548319000063 10.1017/S0963548399003752 10.1016/j.jctb.2017.09.001 10.1137/141002177 10.1002/jgt.20155 10.1016/j.disc.2011.11.031 10.1016/j.disc.2013.07.014 10.1016/j.ejc.2014.05.003 10.1002/jgt.21731 10.1002/jgt.21659 10.1002/jgt.21886 10.1002/jgt.20467 10.1016/S0012-365X(99)00145-4 10.1016/j.disc.2017.06.014 10.1016/j.jctb.2013.10.002 10.1016/j.ejc.2009.11.013 10.1134/S0037446617010049 10.1112/jlms.12127 |
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