Let G be a graph and let \(f_i, i \in \{1,\ldots ,s\},\) be a function from V(G) to the set of nonnegative integers. In Sittitrai and Nakprasit (Analogue of DP-coloring on variable degeneracy and its applications, 2020), the concept of DP-F-coloring, a generalization of DP-coloring and variable degeneracy, was introduced. We use DP-F-coloring to define DPG-[k, t]-colorable graphs and modify the proofs in Liu et al. (Graphs Combin 35(3), 695–705, 2019), Sittitrai and Nakprasit (Bull Malays Math Sci Soc, 2019, https://doi.org/10.1007/s40840-019-00800-1), Thomassen (J Combin Theory Ser B 62, 180–181, 1994) to obtain more results on list coloring, DP-coloring, list-forested coloring, and variable degeneracy.

令G为图，令\（f_i，i \ in \ {1，\ ldots，s \}，\）为从V（G）到非负整数集合的函数。的DP-概念在Sittitrai和Nakprasit（可变简并性及其应用，2020的模拟DP着色）˚F -coloring，DP-着色和可变简并性的概括，进行了介绍。我们使用DP- F着色定义DPG- [ k，  t]可着色的图形并修改Liu等人的证明。（Graphs Combin 35（3），695–705，2019），Sittitrai and Nakprasit（Bull Malays Math Sci Soc，2019，https://doi.org/10.1007/s40840-019-00800-1），Thomassen（J Combin） Theory Ser B 62，180–181，1994）在列表着色，DP着色，列表林着色和可变简并性方面获得了更多的结果。