A result in asymmetric Euclidean Ramsey theory

Andrii Arman; Sergei Tsaturian

doi:10.1016/j.disc.2017.10.015

A result in asymmetric Euclidean Ramsey theory

Andrii Arman, Sergei Tsaturian

Research output: Contribution to journal › Article › Research › peer-review

Abstract

It is proved that if the points of the three-dimensional Euclidean space are coloured with red and blue, then there exist either two red points at unit distance, or six collinear blue points with distance one between any two consecutive points.

Original language	English
Pages (from-to)	1502-1508
Number of pages	7
Journal	Discrete Mathematics
Volume	341
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2017.10.015
Publication status	Published - 1 May 2018
Externally published	Yes

Keywords

Discrete geometry
Euclidean Ramsey
Ramsey

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10.1016/j.disc.2017.10.015

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Cite this

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abstract = "It is proved that if the points of the three-dimensional Euclidean space are coloured with red and blue, then there exist either two red points at unit distance, or six collinear blue points with distance one between any two consecutive points.",

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