English

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 (Δ+2)(\Delta+2)-colorable for large enough Δ\Delta. In fact, we prove the stronger statement that such graphs are square (Δ+2)(\Delta+2)-choosable and even square (Δ+2)(\Delta+2)-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