Equally spaced collinear points in Euclidean Ramsey theory
Combinatorics
2017-05-17 v2 Metric Geometry
Abstract
It is proved that for , if the points of -dimensional Euclidean space are coloured in red and blue, then there are either two red points distance one apart or blue collinear points with distance one between any two consecutive points. This result is new for .
Keywords
Cite
@article{arxiv.1705.04640,
title = {Equally spaced collinear points in Euclidean Ramsey theory},
author = {Andrii Arman and Sergei Tsaturian},
journal= {arXiv preprint arXiv:1705.04640},
year = {2017}
}