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arXiv · 1309.6710

On the number of spanning trees in random regular graphs

Catherine Greenhill·Matthew Kwan·David Wind
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Abstract

Let $d \geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture.

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Catherine Greenhill, Matthew Kwan, David Wind. 2014-02-18. On the number of spanning trees in random regular graphs. https://doi.org/10.37236/3752

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