DP-colorings of graphs with high chromatic number

DP-coloring is a generalization of list coloring introduced recently by Dvořák and Postle (2015). We prove that for every n-vertex graph G whose chromatic number χ(G) is “close” to n, the DP-chromatic number of G equals χ(G). “Close” here means χ(G)≥n−O(n), and we also show that this lower bound is best possible (up to the constant factor in front of n), in contrast to the case of list coloring.