The asymptotic distribution of short cycles in random regular graphs
نویسندگان
چکیده
منابع مشابه
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 corresp...
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The asymptotic distribution of small subgraphs of a random graph has been basically worked out (see Ruciński [5] for example). But for random regular graphs, the main techniques for proving, for instance, asymptotic normality, do not seem to be usable. One very recent result in this direction is to be found in [3], where switchings were applied to cycle counts. The aim of the present note is to...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1981
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(81)80022-6