Tiling the plane with hexagons: improved separations for $k$-colourings
Combinatorics
2022-06-28 v1
Abstract
It has been common knowledge since 1950 that seven colours can be assigned to tiles of an infinite honeycomb with cells of unit diameter such that no two tiles of the same colour are closer than apart. Various authors have described tilings using colours, giving corresponding values for , but it is generally unknown whether these are the largest possible for a given . Here, for many , we describe tilings with larger values of than previously reported.
Keywords
Cite
@article{arxiv.2206.12635,
title = {Tiling the plane with hexagons: improved separations for $k$-colourings},
author = {Aubrey D. N. J. de Grey and Jaan Parts},
journal= {arXiv preprint arXiv:2206.12635},
year = {2022}
}