Let Tn denote a tree with n nodes that is rooted at node r. (For definitions not given here see [4] or [10].) The altitude of a node u in Tn is the distance α = α (u, Tn) between r and u in Tn. The width of Tn at altitude is the number Wk = Wk(Tn) of nodes at altitude in Tn, where = 0, 1, …