Constant Time Generation of Trees with Degree Bounds

Given a number n of vertices, a lower bound d on the diameter, and a capacity function Delta(k) >= 2, k = 0, 1, ... , [n/2], we consider the problem of enumerating all unrooted trees T with exactly n vertices and a diameter at least d such that the degree of each vertex with distance k from the center of T is at most Delta(k). We give an algorithm that generates all such trees without duplication in O(1)-time delay per output in the worst case using O(n) space.