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The diameter of the uniform spanning tree of dense graphs
Published online by Cambridge University Press: 13 May 2022
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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- © The Author(s), 2022. Published by Cambridge University Press
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