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Mat. Tr., 2018, Volume 21, Number 2, Pages 61–71 (Mi mt338)  

On differences between DP-coloring and list coloring

A. Yu. Bernshteyna, A. V. Kostochkaab

a University of Illinois at Urbana-Champaign, Urbana, IL, USA
b Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

Abstract: DP-Coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle [12]. Many known upper bounds for the list-chromatic number extend to the DP-chromatic number, but not all of them do. In this note we describe some properties of DP-coloring that set it aside from list coloring. In particular, we give an example of a planar bipartite graph with DP-chromatic number $4$ and prove that the edge-DP-chromatic number of a $d$-regular graph with $d\geq2$ is always at least $d+1$.

Key words: list coloring of a graph, edge coloring, DP-coloring of a graph.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00353_a
16-01-00499_a
National Science Foundation DMS-1600592
The work of the first author was partially supported by the Illinois Distinguished Fellowship. The work of the second author was partially supported by the Russian Foundation for Basic Research (projects 18-01-00353 and 16-01-00499) and by the National Science Foundation (project DMS-1600592).


DOI: https://doi.org/10.17377/mattrudy.2018.21.202

Full text: PDF file (258 kB)
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English version:
Siberian Advances in Mathematics, 2019, 29, 183–189

UDC: 519.17
Received: 18.12.2017

Citation: A. Yu. Bernshteyn, A. V. Kostochka, “On differences between DP-coloring and list coloring”, Mat. Tr., 21:2 (2018), 61–71; Siberian Adv. Math., 29 (2019), 183–189

Citation in format AMSBIB
\Bibitem{BerKos18}
\by A.~Yu.~Bernshteyn, A.~V.~Kostochka
\paper On differences between DP-coloring and list coloring
\jour Mat. Tr.
\yr 2018
\vol 21
\issue 2
\pages 61--71
\mathnet{http://mi.mathnet.ru/mt338}
\crossref{https://doi.org/10.17377/mattrudy.2018.21.202}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\pages 183--189
\crossref{https://doi.org/10.3103/S1055134419030039}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071428401}


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