The Johansson‐Molloy theorem for DP‐coloring

The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for triangle‐free graphs G, avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit...

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Vydáno v:Random structures & algorithms Ročník 54; číslo 4; s. 653 - 664
Hlavní autor: Bernshteyn, Anton
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York John Wiley & Sons, Inc 01.07.2019
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Témata:
Coloring
DP‐coloring
entropy compression
Graph coloring
list coloring
Local Lemma
triangle‐free graphs
ISSN:1042-9832, 1098-2418
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Shrnutí:The aim of this note is twofold. On the one hand, we present a streamlined version of Molloy's new proof of the bound χ(G)≤(1+o(1))Δ(G)/lnΔ(G) for triangle‐free graphs G, avoiding the technicalities of the entropy compression method and only using the usual “lopsided” Lovász Local Lemma (albeit in a somewhat unusual setting). On the other hand, we extend Molloy's result to DP‐coloring (also known as correspondence coloring), a generalization of list coloring introduced recently by Dvořák and Postle.
Bibliografie:ObjectType-Article-1
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20811