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Random Graph Processes with Degree Restrictions

Published online by Cambridge University Press:  12 September 2008

A. Ruciński  and
N. C. Wormald
A. Ruciński
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Matejki 48–49, 60–769 Poznań, Poland
N. C. Wormald
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, VIC 3052, Australia
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Abstract

Suppose that a 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 bounded above by d. We prove that if n → ∞ with d fixed, then with probability tending to 1, the final result of this process is a graph with ⌊nd / 2⌋ edges.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 2 , June 1992 , pp. 169 - 180
Copyright
Copyright © Cambridge University Press 1992

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