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Shape Measures of Random Increasing k-trees†

Part of: Graph theory Limit theorems Combinatorial probability

Published online by Cambridge University Press:  04 May 2016

ALEXIS DARRASSE ,
HSIEN-KUEI HWANG  and
MICHÈLE SORIA
ALEXIS DARRASSE
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, LIP6, F-75005, Paris, France (e-mail: darrasse@gmail.com, michele.soria@lip6.fr)
HSIEN-KUEI HWANG
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 115Taiwan (e-mail: hkhwang@stat.sinica.edu.tw)
MICHÈLE SORIA
Affiliation:
Sorbonne Universités, UPMC Univ. Paris 06, LIP6, F-75005, Paris, France (e-mail: darrasse@gmail.com, michele.soria@lip6.fr)
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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.

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems 05C80: Random graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 5 , September 2016 , pp. 668 - 699
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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