DP-coloring (also known as correspondence coloring) is a generalization of
list coloring introduced recently by Dvo\v{r}\'ak and Postle (2017). In this
paper, we prove that every planar graph G without 4-cycles adjacent to
k-cycles is DP-4-colorable for k=5 and 6. As a consequence, we obtain
two new classes of 4-choosable planar graphs. We use identification of
verticec in the proof, and actually prove stronger statements that every
pre-coloring of some short cycles can be extended to the whole graph.Comment: 12 page
