小独立数图形中的 H 因子

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-31 DOI:10.1016/j.jctb.2024.07.005

Ming Chen , Jie Han , Guanghui Wang , Donglei Yang

引用次数: 0

摘要

设 H 是一个 h 顶点图。H 的顶点嵌套度 ar(H) 是最小整数 r，使得 V(H) 可以被分割成 r 部分，且每个部分都在 H 中诱导出一个森林。我们证明，对于足够大的 n∈hN，δ(G)≥max{(1-2f(H)+o(1))n,(12+o(1))n} 且 α(G)=o(n)的每个 n 顶点图 G 都包含一个 H 因子，其中 f(H)=2ar(H) 或 2ar(H)-1。这一结果可以看作是拉姆齐-图兰理论中的阿隆-尤斯特定理[1]，它概括了巴洛格-莫拉-谢里夫扎德[2]和克尼林-苏[21]关于簇因子的结果。特别是，对于无限多的非小块图 H 来说，度条件是渐近尖锐的。

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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H-factors in graphs with small independence number

Let H be an h-vertex graph. The vertex arboricity $a r (H)$ of H is the least integer r such that $V (H)$ can be partitioned into r parts and each part induces a forest in H. We show that for sufficiently large $n \in h N$ , every n-vertex graph G with $δ (G) \geq \max {(1 - \frac{2}{f (H)} + o (1)) n, (\frac{1}{2} + o (1)) n}$ and $α (G) = o (n)$ contains an H-factor, where $f (H) = 2 a r (H)$ or $2 a r (H) - 1$ . The result can be viewed an analogue of the Alon–Yuster theorem [1] in Ramsey–Turán theory, which generalizes the results of Balogh–Molla–Sharifzadeh [2] and Knierim–Su [21] on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs H which are not cliques.

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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.