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February 1997 Random graph processes with maximum degree $2$
A. Ruciński, N. C. Wormald
Ann. Appl. Probab. 7(1): 183-199 (February 1997). DOI: 10.1214/aoap/1034625259

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 at most 2. In a previous article, the authors showed that as $n \to \infty$, with probability tending to 1, the result of this process is a graph with n edges. The number of l-cycles in this graph is shown to be asymptotically Poisson $(1 \geq 3)$, and other aspects of this random graph model are studied.

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A. Ruciński. N. C. Wormald. "Random graph processes with maximum degree $2$." Ann. Appl. Probab. 7 (1) 183 - 199, February 1997. https://doi.org/10.1214/aoap/1034625259

Information

Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0981.05090
MathSciNet: MR1428756
Digital Object Identifier: 10.1214/aoap/1034625259

Subjects:
Primary: 05C80 , 05C85

Keywords: Generation algorithms , limiting distributions , number of cycles

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 1 • February 1997
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