English

Progressions in Euclidean Ramsey theory

Combinatorics 2024-12-17 v2

Abstract

Conlon and Wu showed that there is a red/blue-coloring of En\mathbb{E}^n that does not contain 33 red collinear points separated by unit distance and m=1050m=10^{50} blue collinear points separated by unit distance. We prove that the statement holds with m=1177m=1177. We show similar results with different distances between the points.

Keywords

Cite

@article{arxiv.2402.12567,
  title  = {Progressions in Euclidean Ramsey theory},
  author = {Jakob Führer and Géza Tóth},
  journal= {arXiv preprint arXiv:2402.12567},
  year   = {2024}
}
R2 v1 2026-06-28T14:53:49.483Z