English

Equally spaced collinear points in Euclidean Ramsey theory

Combinatorics 2017-05-17 v2 Metric Geometry

Abstract

It is proved that for k4k\geq 4, if the points of kk-dimensional Euclidean space are coloured in red and blue, then there are either two red points distance one apart or k+3k+3 blue collinear points with distance one between any two consecutive points. This result is new for 4k104\leq k\leq 10.

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}
}