Suppose that T is an Sk-tree with handle v. Show that T can be obtained from disjoint trees T0, T1, . . . , Tk−1, with roots r0, r1, . . . , rk−1, respectively, where v is not in any of these trees, where Ti is an Si -tree for i = 0, 1, . . . , k − 1, by connecting v to r0 and ri to ri+1 for i = 0, 1, . . . , k − 2.