  An interesting generalization of list coloring is so called DP-coloring
(named after Dvo\v{r}\'ak and Postle). We study $(i,j)$-defective DP-colorings
of simple graphs. Define $g_{DP}(i,j,n)$ to be the minimum number of edges in
an $n$-vertex DP-$(i,j)$-critical graph. We prove sharp bounds on
$g_{DP}(i,j,n)$ for $i=1,2$ and $j\geq 2i$ for infinitely many $n$.
