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The asymptotic distribution of long cycles in random regular graphs

✍ Scribed by Hans Garmo

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 580 KB
Volume: 15
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199908)15:1<43::aid-rsa3>3.0.co;2-s

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✦ Synopsis

The asymptotic distribution of the number of cycles of length l in a random r-regular graph is determined. The length of the cycles is defined as a function of the Ž . Ž . number of vertices n, thus l s l n , and the length satisfies l n ª ϱ as n ª ϱ. The limiting Ž .

Ž . distribution turns out to depend on whether l n rnª 0 or l n rnª q, 0-q -1 as n ª ϱ. In the first case the limit distribution is a weighted sum of Poisson variables while in the other case the limit distribution is similar to the limit distribution of Hamiltonian cycles in a random r-regular graph.

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