On minimal universal trees

In this paper we solve the problem of finding a minimal n-universal rooted tree. We show that the numberα(n) of vertices of a minimal n-universal rooted tree coincides with the quantity of trees of a special form (uniform trees), the number of whose vertices ≤n. We derive a recursion formula for computing the value ofα(n). We also specify the construction of a minimal universal tree for an arbitrary set of uniform trees.