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arXiv · 2009.09656

The diameter of the uniform spanning tree of dense graphs

Noga Alon·Asaf Nachmias·Matan Shalev
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Abstract

We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on $n$ vertices with minimal degree linear in $n$ is typically of order $\sqrt{n}$. A byproduct of our proof, which is of independent interest, is that on such graphs the Cheeger constant and the spectral gap are comparable.

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Noga Alon, Asaf Nachmias, Matan Shalev. 2020-09-21. The diameter of the uniform spanning tree of dense graphs. https://arxiv.org/abs/2009.09656

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