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Random labelled trees and their branching networks

Part of: Graph theory Markov processes

Published online by Cambridge University Press:  09 April 2009

G. R. Grimmett
G. R. Grimmett
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, England
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Abstract

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A random rooted labelled tree on n vertices has asymptotically the same shape as a branching-type process, in which each generation of a branching process with Poisson family sizes, parameter one, is supplemented by a single additional member added at random to one of the families in that generation. In this note we use this probabilistic representation to deduce the asymptotic distribution of the distance from the root to the nearest endertex other than itself.

Keywords

random treerandom graphbranching process

MSC classification

Secondary: 05C05: Trees 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 229 - 237
Copyright
Copyright © Australian Mathematical Society 1980

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