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arXiv · 2306.06243

Maximum number of symmetric extensions in the random graph

Stepan Vakhrushev·Maksim Zhukovskii
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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 $k$-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.

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Stepan Vakhrushev, Maksim Zhukovskii. 2023-06-09. Maximum number of symmetric extensions in the random graph. https://arxiv.org/abs/2306.06243

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