2024/12/12 by Luke Postle, Postle, Luke, Evelyne Smith‐Roberge +3
Computer Science · Engineering · #Advanced Graph Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2412.09410
A (vertex) colouring of graph is 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.