✦ LIBER ✦
Packing and covering constants for certain families of trees. I
✍ Scribed by A. Meir; J. W. Moon
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 518 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
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.