Counting graphic sequences

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• Paul Balister (Oxford)
• Thursday 18 May 2023, 14:00-15:00
• MR12.

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Note 2pm start

Given an integer $n$, let $G(n)$ be the number of integer sequences $n−1≥d_1≥d_2≥⋯≥d_n≥0$ that are the degree sequence of some graph. We show that $G(n)=(c+o(1))4^n/n{3/4}$ for some constant $c>0$, improving both the previously best upper and lower bounds by a factor of $n^{1/4+o(1)}$. The proof relies on a translation of the problem into one concerning integrated random walks.

Joint work with Serte Donderwinkel, Carla Groenland, Tom Johnston and Alex Scott.

This talk is part of the Combinatorics Seminar series.

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