  Correspondence coloring, or DP-coloring, is a generalization of list coloring
introduced recently by Dvo\v{r}\'{a}k 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.
