The Annals of Applied Probability

Random graph processes with maximum degree $2$

A. Ruciński and N. C. Wormald

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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.

Article information

Ann. Appl. Probab., Volume 7, Number 1 (1997), 183-199.

First available in Project Euclid: 14 October 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20] 05C85: Graph algorithms [See also 68R10, 68W05]

Generation algorithms number of cycles limiting distributions


Ruciński, A.; Wormald, N. C. Random graph processes with maximum degree $2$. Ann. Appl. Probab. 7 (1997), no. 1, 183--199. doi:10.1214/aoap/1034625259.

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