Packing and covering constants for certain families of trees. I

If ℱ denotes a family of rooted trees, let pk(n) and ck(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 pk(n)/n and ck(n)/n as n ∞ exist and we describe how to evaluate these limits.