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arXiv · 1705.04640

Equally spaced collinear points in Euclidean Ramsey theory

Andrii Arman·Sergei Tsaturian
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Abstract

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

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Andrii Arman, Sergei Tsaturian. 2017-05-15. Equally spaced collinear points in Euclidean Ramsey theory. https://arxiv.org/abs/1705.04640

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