Approximate path decompositions of regular graphs

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-18 DOI:10.1112/jlms.70269

Richard Montgomery, Alp Müyesser, Alexey Pokrovskiy, Benny Sudakov

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引用次数: 0

Abstract

We show that the edges of any $d$ -regular graph can be almost decomposed into paths of length roughly $d$ , giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$ -regular graph can be partitioned into $n / (d + 1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009.

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正则图的近似路径分解

我们证明了任意d$ d$正则图的边几乎可以分解成长度大致为d$ d$的路径，并给出了1957年Kotzig问题的近似解。在此过程中，我们证明了d$ d$正则图的几乎所有顶点都可以划分为n/(d+1)$ n/(d+1)$路径，渐近地证实了Magnant和Martin从2009年提出的一个猜想。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.