Short Cycles in Random Regular Graphs
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004