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Connectedness of graphs generated by a random d-process

Part of: Special processes Graph theory

Published online by Cambridge University Press:  09 April 2009

A. Ruciński  and
N. C. Wormald
A. Ruciński
Affiliation:
Department of Discrete Mathematics, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48–49, 60–769 Poznań, Poland e-mail: rucinski@amu.edu.pl
N. C. Wormald
Affiliation:
Department of Mathematics, and Statistics, The University of Melbourne, VIC 3010, Australia e-mail: nick@ms.unimelb.edu.au
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Abstract

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Suppose that a graph process begins with n isolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at most d. In a previous article, the authors showed that as n → ∞, with probability tending to 1, the result of this process is a d-regular graph. This graph is shown to be connected with probability asymptotic to 1.

MSC classification

Secondary: 05C80: Random graphs 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 67 - 86
Copyright
Copyright © Australian Mathematical Society 2002

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