Stochastic embeddings of graphs into trees

IF 1.1 2区数学 Q1 MATHEMATICS

Banach Journal of Mathematical Analysis Pub Date : 2024-07-26 DOI:10.1007/s43037-024-00373-7

Th. Schlumprecht, G. Tresch

引用次数: 0

Abstract

It is known that every graph with n vertices embeds stochastically into trees with distortion \(O(\log n)\). In this paper, we show that this upper bound is sharp for a large class of graphs. As this class of graphs contains Laakso graphs, this result extends known examples that obtain this largest possible stochastic distortion.

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图到树的随机嵌入

众所周知，每一个有 n 个顶点的图都会随机嵌入扭曲度为 \(O(\log n)\)的树。在本文中，我们证明了这一上限对于一大类图来说是尖锐的。由于这一类图中包含了拉克索图，因此这一结果扩展了获得最大随机失真度的已知例子。

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

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.