Every planar graph without adjacent cycles of length at most $8$ is $3$-choosable
Combinatorics
2019-07-17 v2
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 is -choosable, which extends this result of Dvo\v{r}\'{a}k and Postle.
Cite
@article{arxiv.1804.03976,
title = {Every planar graph without adjacent cycles of length at most $8$ is $3$-choosable},
author = {Runrun Liu and Xiangwen Li},
journal= {arXiv preprint arXiv:1804.03976},
year = {2019}
}
Comments
12 pages,1 figure, published on European J. Combin