Improved bounds for lines and $1$-separated sets in Euclidean Ramsey theory

Gabriel Currier, Param Mody, Zehan Xie +1

Let $K$ be a $1$-separated set of diameter at most $R-1$, and let ${\ell }_m$ denote a collection of $m$ points on a line, with consecutive points of distance $1$ apart. Conlon and Fo…