The diameter-three conjecture for small Weyl graphs

Let $\Phi$ be an irreducible classical root system of rank at least $2$, and let $\Gamma_s(\Phi)$ be its small Weyl graph. The diameter of a graph is the maximum distance between two of its vertices. Diameter-three conjecture. The diameter of $\Gamma_s(\Phi)$ is at most $3$. This is suggested by computations for several root systems, in which the diameter was always at most $3$; the general case remains open.