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COMBINATORICS
2004

Short Cycles in Random Regular Graphs

8 years 5 months ago
Short Cycles in Random Regular Graphs
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution similar to that of independent Poisson variables. In particular, we find the asymptotic probability that there are no cycles with sizes in a given set, including the probability that the girth is greater than g. A corresponding result is given for random regular bipartite graphs.
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMBINATORICS
Authors Brendan D. McKay, Nicholas C. Wormald, Beata Wysocka
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