如何建造支柱：托马森猜想的证明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-01 DOI:10.1016/j.jctb.2023.04.004

Irene Gil Fernández , Hong Liu

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引用次数: 7

摘要

Carsten Thomassen在1989年推测，如果一个图的最小度远大于宇宙中原子的数量（δ（G）≥101010），那么它包含一个柱，这是一个由两个相同长度的顶点不相交循环组成的图，例如，s，以及s个相同长度的顶点不交路径3，它们按循环周围的顺序连接匹配的顶点。尽管在过去的三十年里，支柱的结构很简单，路径和循环的强大嵌入方法也有了各种发展，但迄今为止，这个看起来天真无邪的猜想没有取得任何进展。在本文中，我们通过在次线性扩展器中建立一个支柱（算法）来证明这个猜想。

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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How to build a pillar: A proof of Thomassen's conjecture

Carsten Thomassen in 1989 conjectured that if a graph has minimum degree much more than the number of atoms in the universe ( $δ (G) \geq 10^{10^{10}}$ ), then it contains a pillar, which is a graph that consists of two vertex-disjoint cycles of the same length, s say, along with s vertex-disjoint paths of the same length³ which connect matching vertices in order around the cycles. Despite the simplicity of the structure of pillars and various developments of powerful embedding methods for paths and cycles in the past three decades, this innocent looking conjecture has seen no progress to date. In this paper, we give a proof of this conjecture by building a pillar (algorithmically) in sublinear expanders.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.