The diameter of the uniform spanning tree of dense graphs

Noga Alon, Asaf Nachmias, Matan Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 √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.

Original languageEnglish
Pages (from-to)1010-1030
Number of pages21
JournalCombinatorics Probability and Computing
Volume31
Issue number6
DOIs
StatePublished - Nov 2022

Funding

FundersFunder number
Simons Foundation
Israel Science Foundation1294/19, 1207/15
National Science FoundationDMS-1855464
European Research Council676970
United States-Israel Binational Science Foundation2018267

    Keywords

    • dense graphs
    • spectral gap
    • Uniform spanning trees

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