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A generalization of list-coloring, now known as DP-coloring, was recentlyintroduced by Dvo\v{r}\'{a}k and Postle. Essentially, DP-coloring assigns anarbitrary matching between lists of colors at adjacent vertices, as opposed toonly matching identical colors as is done for list-coloring. Several results onlist-coloring of planar graphs have since been extended to the setting ofDP-coloring. We note that list-coloring results do not always extend toDP-coloring results. Our main result in this paper is to prove that everyplanar graph without cycles of length $\{4, a, b, 9\}$ for $a, b \in \{6, 7,8\}$ is DP-$3$-colorable, extending three existing results on $3$-choosabilityof planar graphs.

DP-3-coloring of planar graphs without $4,9$-cycles and two cycles from $\{5,6,7,8\}$