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Shape Measures of Random Increasing k-trees

Published online by Cambridge University Press:  04 May 2016

ALEXIS DARRASSE
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, LIP6, F-75005, Paris, France (e-mail: [email protected], [email protected])
HSIEN-KUEI HWANG
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 115Taiwan (e-mail: [email protected])
MICHÈLE SORIA
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, LIP6, F-75005, Paris, France (e-mail: [email protected], [email protected])

Abstract

Random increasing k-trees represent an interesting and useful class of strongly dependent graphs that have been studied widely, including being used recently as models for complex networks. In this paper we study an informative notion called BFS-profile and derive, by several analytic means, asymptotic estimates for its expected value, together with the limiting distribution in certain cases; some interesting consequences predicting more precisely the shapes of random k-trees are also given. Our methods of proof rely essentially on a bijection between k-trees and ordinary trees, the resolution of linear systems, and a specially framed notion called Flajolet–Odlyzko admissibility.

Type
Paper
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

A complete version containing an appendix on zero distribution of the indicial polynomial and another on random generation of random k-trees can be found on the second author's webpage. This version will be referred to as DHS throughout this paper.

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