Generalized DP-colorings of graphs

In the present paper we extend following three coloring concepts for class of finite undirected graphs having multiple edges but no loops. First all, generalized concept, in which same colored vertices a graph induce subgraph satisfying prescribed property. Secondly, concept variable degeneracy, was introduced by Borodin, Kostochka and Toft 2000; this makes it possible to give common generalization point partition number list chromatic number. Finally, DP-coloring as Ďvorák Postle 2018, where assignment is replaced cover. Combining these leads generalizations various classical results, including theorems Brooks, Gallai, Erdős, Rubin Taylor. Our main result DP-version theorem about partitions into fixed induced subgraphs with bounded degeneracy due Kostochka, Toft.