Defective DP-colorings of sparse simple graphs

DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle. We introduce and study \((i,j)\)-defective DP-colorings of simple graphs. Let \(g_{DP}(i,j,n)\) be the minimum number of edges in an \(n\)-vertex DP-\((i,j)\)-critical graph. In this paper we determine sharp bound on \(g_{DP}(i,j,n)\) for each \(i\geq3\) and \(j\geq 2i+1\) for infinitely many \(n\).