Classical problems in hypergraph coloring theory are to estimate the minimum number of edges, (respectively, ), in a non-2-colorable -uniform (respectively, -uniform and simple) hypergraph. The best currently known bounds are for any fixed and some , , , (where may depend on ). In this paper we consider the same problems in the context of DP-coloring (also known as correspondence coloring), which is a generalization of list coloring introduced by Dvořák and Postle and related to local conflict coloring studied independently by Fraigniaud, Heinrich, and Kosowski. Let (respectively, ) denote the minimum number of edges in a non-2-DP-colorable -uniform (respectively, -uniform and simple) hypergraph. By definition, and .
While the proof of the bound due to Erdős and Lovász also works for , we show that the trivial lower bound is asymptotically tight, i.e., . On the other hand, when is even, we prove that the lower bound is not sharp, i.e., . Whether this result holds for infinitely many odd values of remains an open problem. Nevertheless, we conjecture that the difference can be arbitrarily large.