Planar graphs have bounded nonrepetitive chromatic number
Combinatorics
2022-01-24 v4 Discrete Mathematics
Abstract
A colouring of a graph is "nonrepetitive" if for every path of even order, the sequence of colours on the first half of the path is different from the sequence of colours on the second half. We show that planar graphs have nonrepetitive colourings with a bounded number of colours, thus proving a conjecture of Alon, Grytczuk, Haluszczak and Riordan (2002). We also generalise this result for graphs of bounded Euler genus, graphs excluding a fixed minor, and graphs excluding a fixed topological minor.
Cite
@article{arxiv.1904.05269,
title = {Planar graphs have bounded nonrepetitive chromatic number},
author = {Vida Dujmović and Louis Esperet and Gwenaël Joret and Bartosz Walczak and David R. Wood},
journal= {arXiv preprint arXiv:1904.05269},
year = {2022}
}