Every planar graph without adjacent cycles of length at most $8$ is $3$-choosable

Abstract

DP-coloring as a generalization of list coloring was introduced by Dvo\v{r}\'{a}k and Postle in 2017, who proved that every planar graph without cycles from 4 to 8 is 3-choosable, which was conjectured by Borodin {\it et al.} in 2007. In this paper, we prove that every planar graph without adjacent cycles of length at most $8$ is $3$-choosable, which extends this result of Dvo\v{r}\'{a}k and Postle.