Planar Graphs of Girth at least Five are Square $(\Delta + 2)$-Choosable
Combinatorics
2019-11-18 v2
Abstract
We prove a conjecture of Dvo\v{r}\'ak, Kr\'al, Nejedl\'y, and \v{S}krekovski that planar graphs of girth at least five are square -colorable for large enough . In fact, we prove the stronger statement that such graphs are square -choosable and even square -paintable.
Keywords
Cite
@article{arxiv.1508.03663,
title = {Planar Graphs of Girth at least Five are Square $(\Delta + 2)$-Choosable},
author = {Marthe Bonamy and Daniel W. Cranston and Luke Postle},
journal= {arXiv preprint arXiv:1508.03663},
year = {2019}
}
Comments
22 pages, 7 figures; this version incorporates reviewer feedback: fixed and rewrote proof of Lemma 3.5, expanded Section 4; to appear in J. Combin. Theory Ser. B