Intransitive trees

Abstract

We study the class of trees T on the set {1, 2, ..., n} such that for any 1 ≤ i < j < k ≤ n the pairs {i, j} and {j, k} cannot both be edges in T. We derive a formula for the number of such trees. We also give a functional equation and a differential equation for the generating function. We mention some additional combinatorial interpretations of these numbers. © 1997 Academic Press.