Hamilton cycles in dense regular digraphs and oriented graphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-04 DOI:10.1016/j.jctb.2023.09.004

Allan Lo , Viresh Patel , Mehmet Akif Yıldız

引用次数: 2

Abstract

We prove that for every $ε > 0$ there exists $n_{0} = n_{0} (ε)$ such that every regular oriented graph on $n > n_{0}$ vertices and degree at least $(1 / 4 + ε) n$ has a Hamilton cycle. This establishes an approximate version of a conjecture of Jackson from 1981. We also establish a result related to a conjecture of Kühn and Osthus about the Hamiltonicity of regular directed graphs with suitable degree and connectivity conditions.

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稠密正则有向图和有向图中的Hamilton环

我们证明了对于每个ε>；0存在n0=n0（ε），使得n>；n0个顶点和次数至少为（1/4+ε）n有一个Hamilton循环。这建立了杰克逊1981年猜想的近似版本。我们还建立了一个与Kühn和Osthus关于具有适当度和连通条件的正则有向图的哈密顿性的猜想有关的结果。

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

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.