The Johansson‐Molloy theorem for DP‐coloring. Issue 4 (7th November 2018)

• Record Type: Journal Article
• Authors: Bernshteyn, Anton
• Is Part Of: Random structures & algorithms. Volume 54:Issue 4(2019)
• Page Start: 653
• Page End: 664
• Publication Date: 2018-11-07
• Subjects: Graph coloring -- list coloring -- DP‐coloring -- triangle‐free graphs -- Local Lemma -- entropy compression; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20811
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract : 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 ) / ln Δ ( 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.