  DP-coloring (also known as correspondence coloring) is a generalization of
list coloring introduced recently by Dvo\v{r}\'{a}k and Postle. Many known
upper bounds for the list-chromatic number extend to the DP-chromatic number,
but not all of them do. In this note we describe some unusual properties of
DP-coloring that set it aside from list coloring. In particular, we give an
example of a planar bipartite graph with DP-chromatic number $4$ and prove that
the edge-DP-chromatic number of a $d$-regular graph with $d\geq 2$ is always at
least $d+1$.
