2023/06/09 by Stepan Vakhrushev, Vakhrushev, Stepan, Maksim Zhukovskii +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2306.06243
openalex publication_date 2023/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that after an appropriate rescaling the maximum degree of the binomial random graph converges in distribution to a Gumbel random variable. The same holds true for the maximum number of common neighbours of a k-vertex set, and for the maximum number of s-cliques sharing a single vertex. Can these results be generalised to the maximum number of extensions of a k-vertex set for any given way of extending of a k-vertex set by an s-vertex set? In this paper, we generalise the above mentioned results to a class of ``symmetric extensions'' and show that the limit distribution is not necessarily from the Gumbel family.