𝔖 Bobbio Scriptorium
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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

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✦ 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.