Progressions in Euclidean Ramsey theory

Abstract

Conlon and Wu showed that there is a red/blue-coloring of ${\mathbb{E}}^n$ that does not contain $3$ red collinear points separated by unit distance and $m=10^{50}$ 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.