Planar Graphs of Girth at least Five are Square $(Δ+ 2)$-Choosable
Marthe Bonamy, Daniel W. Cranston, Luke Postle · arXiv (Cornell University) · 2015
We prove a conjecture of Dvořák, Král, Nejedlý, and Škrekovski that planar graphs of girth at least five are square $(Δ+2)$-colorable for large enough $Δ$. In fact, we prove the stronger statement that such graphs are square $(Δ+2)$-choosable and even square $(Δ+2)$-paintable.