Maximum number of symmetric extensions in the random graph
Combinatorics
2023-06-13 v1 Probability
Abstract
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 -vertex set, and for the maximum number of -cliques sharing a single vertex. Can these results be generalised to the maximum number of extensions of a -vertex set for any given way of extending of a -vertex set by an -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.
Keywords
Cite
@article{arxiv.2306.06243,
title = {Maximum number of symmetric extensions in the random graph},
author = {Stepan Vakhrushev and Maksim Zhukovskii},
journal= {arXiv preprint arXiv:2306.06243},
year = {2023}
}