Seog-Jin Kim (김석진), Online DP-coloring of graphs

Online list coloring and DP-coloring are generalizations of list coloring that attracted considerable attention recently. Each of the paint number, ${\chi }_P(G)$, (the minimum number of colors needed for an online coloring of $G$) and the DP-chromatic number, ${\chi }_{DP}(G)$, (the minimum number of colors needed for a DP-coloring of $G$) is at least the list chromatic number, ${\chi }_{\ell }(G)$, of $G$ and can be much larger. On the other hand, each of them has a number of useful properties.
We introduce a common generalization, online DP-coloring, of online list coloring and DP-coloring and to study its properties. This is joint work with Alexandr Kostochka, Xuer Li, and Xuding Zhu.