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- W4317465156 abstract "Given an integer $n$, let $G(n)$ be the number of integer sequences $n-1ge d_1ge d_2gedotsbge d_nge 0$ 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 $n^{1/4}$ (up to polylog-factors). Additionally, we answer a question of Royle, extend the values of $n$ for which the exact value of $G(n)$ is known from $nle290$ to $nle 1651$ and determine the asymptotic probability that the integral of a (lazy) simple symmetric random walk bridge remains non-negative." @default.
- W4317465156 created "2023-01-20" @default.
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- W4317465156 date "2023-01-17" @default.
- W4317465156 modified "2023-09-25" @default.
- W4317465156 title "Counting graphic sequences via integrated random walks" @default.
- W4317465156 doi "https://doi.org/10.48550/arxiv.2301.07022" @default.
- W4317465156 hasPublicationYear "2023" @default.
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