Acyclic List Colouring Locally Planar Graphs
Combinatorics
2024-12-13 v1
Abstract
A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi and Mohar proved that locally planar graphs are acyclically 7-colourable. In 2002, Borodin, Fon-Der-Flaass, Kostochka, Raspaud, and Sopena proved that planar graphs are acyclically 7-list-colourable. We prove that locally planar graphs are acyclically 9-list-colourable\textemdash no bound for acyclic list colouring locally planar graphs for any fixed number of colours was previously known.
Keywords
Cite
@article{arxiv.2412.09410,
title = {Acyclic List Colouring Locally Planar Graphs},
author = {Luke Postle and Evelyne Smith-Roberge and Massimo Vicenzo},
journal= {arXiv preprint arXiv:2412.09410},
year = {2024}
}
Comments
19 pages, 4 figures