On the Distribution of the Maximum k-Degrees of the Binomial Random Graph


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For the maximum number Δn of common neighbors of k vertices in the random graph G(n, p), there exist functions an and σn such that \(\frac{\Delta_n - a_n}{\sigma_n}\) converges in distribution to a random variable having the standard Gumbel distribution.

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M. Zhukovskii

Moscow Institute of Physics and Technology (State University); Russian Presidential Academy of National Economy and Public Administration; Caucasus Mathematical Center

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Email: zhukmax@gmail.com
俄罗斯联邦, Dolgoprudnyi, Moscow oblast, 141700; Moscow, 119571; Maikop, 385000 Republic of Adygea

I. Rodionov

Moscow Institute of Physics and Technology (State University); Faculty of Mechanics and Mathematics

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俄罗斯联邦, Dolgoprudnyi, Moscow oblast, 141700; Moscow, 119991

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