The Johansson--Molloy Theorem for DP-Coloring

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 $\chi (G)\le (1+o(1))\Delta (G)/\ln \Delta (G)$ 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.

10 pages, 1 figure; v5: Minor changes following referees' suggestions

References in corpus (2)

• Acyclic edge-coloring using entropy compression
• The asymptotic behavior of the correspondence chromatic number

Cited by in corpus (7)

• Colouring triangle-free graphs with local list sizes
• Cover and variable degeneracy
• Independent transversals in bipartite correspondence-covers
• Variable degeneracy on toroidal graphs
• The $\chi$-Ramsey problem for triangle-free graphs
• Extremal bipartite independence number and balanced coloring
• Uniformly Random Colourings of Sparse Graphs