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Cycles in a Uniform Graph Process†

Published online by Cambridge University Press:  12 September 2008

Jerzy Jaworski  and
Tomasz Łuczak
Jerzy Jaworski
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland.
Tomasz Łuczak
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland.
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Abstract

We study the asymptotic properties of a “uniform” random graph process in which the minimum degree of U(n, M) grows at least as fast as ⌊M/n⌋. We show that if M — n → → ∞, almost surely U(n, M) consists of one giant component and some number of small unicyclic components. We go on to study the distribution of cycles in unicyclic components as they emerge at the beginning of the process and disappear when captured by the giant one.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 223 - 239
Copyright
Copyright © Cambridge University Press 1992

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