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Packing and covering constants for certain families of trees. I
Author(s) -
Meir A.,
Moon J. W.
Publication year - 1977
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190010211
Subject(s) - combinatorics , mathematics , generating function , function (biology) , tree (set theory) , constant (computer programming) , value (mathematics) , discrete mathematics , statistics , computer science , evolutionary biology , biology , programming language
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.