  In this work, we introduce DPG-coloring using the concepts of DP-coloring and
variable degeneracy to modify the proofs on the following papers: (i)
DP-3-coloring of planar graphs without $4$, $9$-cycles and cycles of two
lengths from $\{6, 7, 8\}$ (R. Liu, S. Loeb, M. Rolek, Y. Yin, G. Yu, Graphs
and Combinatorics 35(3) (2019) 695-705), (ii) Every planar graph without
$i$-cycles adjacent simultaneously to $j$-cycles and $k$-cycles is
DP-$4$-colorable when $\{i, j, k\}=\{3, 4, 5\}$ (P. Sittitrai, K. Nakprasit,
arXiv:1801.06760(2019) preprint), (iii) Every planar graph is $5$-choosable (C.
Thomassen, J. Combin. Theory Ser. B 62 (1994) 180-181). Using this
modification, we obtain more results on list coloring, DP-coloring,
list-forested coloring, and variable degeneracy.
