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 chi(G)<=(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" Lovasz 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 Dvorak and Postle.