Sharp Dirac's Theorem for DP-Critical Graphs

Abstract

Correspondence coloring, or DP-coloring, is a generalization of list coloring introduced recently by Dvořák and Postle. In this paper we establish a version of Dirac's theorem on the minimum number of edges in critical graphs in the framework of DP-colorings. A corollary of our main result answers a question posed by Kostochka and Stiebitz on classifying list-critical graphs that satisfy Dirac's bound with equality.

26 pages, 1 figure