DP-3-coloring of planar graphs without $4,9$-cycles and two cycles from $\{5,6,7,8\}$
Combinatorics
2018-09-21 v1
Abstract
A generalization of list-coloring, now known as DP-coloring, was recently introduced by Dvo\v{r}\'{a}k and Postle. Essentially, DP-coloring assigns an arbitrary matching between lists of colors at adjacent vertices, as opposed to only matching identical colors as is done for list-coloring. Several results on list-coloring of planar graphs have since been extended to the setting of DP-coloring. We note that list-coloring results do not always extend to DP-coloring results. Our main result in this paper is to prove that every planar graph without cycles of length for is DP--colorable, extending three existing results on -choosability of planar graphs.
Cite
@article{arxiv.1809.07445,
title = {DP-3-coloring of planar graphs without $4,9$-cycles and two cycles from $\{5,6,7,8\}$},
author = {Runrun Liu and Sarah Loeb and Martin Rolek and Yuxue Yin and Gexin Yu},
journal= {arXiv preprint arXiv:1809.07445},
year = {2018}
}