Sharp Dirac's theorem for DP-critical graphs

Correspondence coloring, or DP-coloring, is a generalization of list coloring introduced recently by Dvoak and Postle [11]. In this article, we establish a version of Dirac's theorem on the minimum number of edges in critical graphs [9] in the framework of DP-colorings. A corollary of our main result answers a question posed by Kostochka and Stiebitz [15] on classifying list-critical graphs that satisfy Dirac's bound with equality.