The diameter of the uniform spanning tree of dense graphs

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2020-09-21 DOI:10.1017/s0963548322000062

N. Alon, Asaf Nachmias, Matan Shalev

引用次数: 6

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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稠密图的一致生成树的直径

我们证明了n个最小线性度的简单连通图的一致生成树的直径通常为$\sqrt{n}$阶。我们证明的一个副产品是，在这样的图上，契格常数和谱隙是可比较的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.