Proof of Schur's conjecture in ${\mathbb{R}}^d$

Andrey B. Kupavskii, Alexandr Polyanskii

In this paper we prove Schur's conjecture in ${\mathbb{R}}^d$, which states that any diameter graph $G$ in the Euclidean space ${\mathbb{R}}^d$ on $n$ vertices may have at most $n$ cliqu…