Packing and covering constants for certain families of trees. I

If ℱ denotes a family of rooted trees, let p k (n) and c k (n) denote the average value of the k ‐packing and k ‐covering numbers of trees in ℱ that have n nodes. We assume, among other things, that the generating function y of trees in ℱ satisfies a relation of the type y = xϕ(y) for some power series ϕ. We show that the limits of p k (n)/n and c k (n)/n as n → ∞ exist and we describe how to evaluate these limits.