On differences between DP-coloring and list coloring

Abstract

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle. Many known upper bounds for the list-chromatic number extend to the DP-chromatic number, but not all of them do. In this note we describe some unusual properties of DP-coloring that set it aside from list coloring. In particular, we give an example of a planar bipartite graph with DP-chromatic number $4$ and prove that the edge-DP-chromatic number of a $d$-regular graph with $d\geq 2$ is always at least $d+1$.

8 pages, 3 figures. arXiv admin note: text overlap with arXiv:1609.09122