Non-spherical sets versus lines in Euclidean Ramsey theory
Combinatorics
2025-09-10 v1
Abstract
We show that for every non-spherical set in , there exists a natural number and a red/blue-colouring of for every such that there is no red copy of X and no blue progression of length with each consecutive point at distance . This verifies a conjecture of Wu and the first author.
Keywords
Cite
@article{arxiv.2406.07718,
title = {Non-spherical sets versus lines in Euclidean Ramsey theory},
author = {David Conlon and Jakob Führer},
journal= {arXiv preprint arXiv:2406.07718},
year = {2025}
}