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arXiv · 2208.13513

More on lines in Euclidean Ramsey theory

David Conlon·Yu-Han Wu
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Abstract

Let $\ell_m$ be a sequence of $m$ points on a line with consecutive points at distance one. Answering a question raised by Fox and the first author and independently by Arman and Tsaturian, we show that there is a natural number $m$ and a red/blue-colouring of $\mathbb{E}^n$ for every $n$ that contains no red copy of $\ell_3$ and no blue copy of $\ell_m$.

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David Conlon, Yu-Han Wu. 2022-12-18. More on lines in Euclidean Ramsey theory. https://arxiv.org/abs/2208.13513

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