Enumerating Alternating Trees

In this paper we examine the enumeration of alternating trees. We give a bijective proof of the fact that the number of alternating unrooted trees with n vertices is given by (1/n2n−1) ∑nk=1 (nk) kn−1, a problem first posed by A. Postnikov (1997, J. Combin. Theory Ser. A79, 360–366). We also show that the number of alternating ordered trees with n vertices is 2(n−1)n−1.