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