## The Annals of Applied Probability

### Random graph processes with maximum degree $2$

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 14 October 2002

https://projecteuclid.org/euclid.aoap/1034625259

Digital Object Identifier
doi:10.1214/aoap/1034625259

Mathematical Reviews number (MathSciNet)
MR1428756

Zentralblatt MATH identifier
0981.05090

#### Citation

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. https://projecteuclid.org/euclid.aoap/1034625259