Progressions in Euclidean Ramsey theory

Conlon and Wu (2022) showed that there is a red/blue-coloring of En that does not contain 3 red collinear points separated by unit distance and m=1050 blue collinear points separated by unit distance. We prove that the statement holds with m=1177. We show similar results with different distances bet...

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Bibliographic Details
Published in:European journal of combinatorics 2025-03, Vol.125, p.104105, Article 104105
Main Authors: Führer, Jakob, Tóth, Géza
Format: Article
Language:English
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Summary:Conlon and Wu (2022) showed that there is a red/blue-coloring of En that does not contain 3 red collinear points separated by unit distance and m=1050 blue collinear points separated by unit distance. We prove that the statement holds with m=1177. We show similar results with different distances between the points.
ISSN:0195-6698
DOI:10.1016/j.ejc.2024.104105