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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 $$\frac{\Delta_n - a_n}{\sigma_n}$$Δn−anσn converges in… Click to show full abstract

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 $$\frac{\Delta_n - a_n}{\sigma_n}$$Δn−anσn converges in distribution to a random variable having the standard Gumbel distribution.

Keywords: distribution maximum; maximum degrees; degrees binomial; binomial random; random graph; distribution

Journal Title: Doklady Mathematics
Year Published: 2018

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