Steiner Minimal Tree for Points on a Circle
D. Z. Du, F. K. Hwang, Shu-Jun Chao · Proceedings of the American Mathematical Society · 1985
We show that the Steiner minimal tree for a set of points on a circle is the shortest path connecting them if at most one distance between two consecutive points is "large". We prove this by making an interesting use of the Steiner ratio $\rho$ which has been well studied in the literature.