A bound of lengths of chains of minimal rational curves on Fano manifolds of Picard number 1

In this paper, we investigate the minimal length of chains of minimal rational curves needed to join two general points on a Fano manifold of Picard number 1 under mild assumptions. In particular, we give a sharp bound of the length by a fundamental argument. As an application, we compute the length for Fano manifolds of dimension ⩽7.