The diameter of the uniform spanning tree of dense graphs

Noga Alon; Asaf Nachmias; Matan Shalev

doi:10.1017/S0963548322000062

The diameter of the uniform spanning tree of dense graphs

Noga Alon
, Asaf Nachmias
, Matan Shalev

Research output: Contribution to journal › Article › peer-review

2 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 language	English
Pages (from-to)	1010-1030
Number of pages	21
Journal	Combinatorics Probability and Computing
Volume	31
Issue number	6
DOIs	https://doi.org/10.1017/S0963548322000062
State	Published - 1 Nov 2022
Externally published	Yes

Keywords

Uniform spanning trees
dense graphs
spectral gap

ASJC Scopus subject areas

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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10.1017/S0963548322000062

Cite this

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title = "The diameter of the uniform spanning tree of dense graphs",

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.",

keywords = "Uniform spanning trees, dense graphs, spectral gap",

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AU - Alon, Noga

AU - Nachmias, Asaf

AU - Shalev, Matan

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PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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.

AB - 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.

KW - Uniform spanning trees

KW - dense graphs

KW - spectral gap

UR - https://www.scopus.com/pages/publications/85146206643

U2 - 10.1017/S0963548322000062

DO - 10.1017/S0963548322000062

M3 - Article

AN - SCOPUS:85146206643

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JO - Combinatorics Probability and Computing

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The diameter of the uniform spanning tree of dense graphs

Abstract

Keywords

ASJC Scopus subject areas

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