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

TL;DR

This paper proves that planar graphs lacking adjacent cycles of length up to 8 are 3-choosable, extending previous results on list coloring and broadening understanding of graph colorability.

Contribution

It establishes that planar graphs without adjacent cycles of length at most 8 are 3-choosable, generalizing earlier findings on cycle restrictions and list coloring.

Findings

Proves planar graphs without adjacent cycles of length ≤8 are 3-choosable

Extends Dvořák and Postle's result on cycle restrictions

Broadens the class of graphs known to be 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.