在 3-Uniform 超图中嵌入松散生成树

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-08 DOI:10.1016/j.jctb.2024.04.003

Yanitsa Pehova , Kalina Petrova

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引用次数: 0

摘要

1995 年，Komlós、Sárközy 和 Szemerédi 发现，每个最小度至少为 (1/2+γ)n 的大 n 顶点图都包含所有有界度的生成树。我们考虑将这一结果推广到 3 图中的松散生成树，即通过连续追加与前一条边共享一个顶点的边而得到的线性超图。我们证明，对于所有 γ 和 Δ 且 n 大的情况，最小顶点度 (5/9+γ)(n2) 的每个 n 顶点 3-Uniform 超图都包含最大顶点度 Δ 的每棵松散生成树 T。

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Embedding loose spanning trees in 3-uniform hypergraphs

In 1995, Komlós, Sárközy and Szemerédi showed that every large n-vertex graph with minimum degree at least $(1 / 2 + γ) n$ contains all spanning trees of bounded degree. We consider a generalization of this result to loose spanning hypertrees in 3-graphs, that is, linear hypergraphs obtained by successively appending edges sharing a single vertex with a previous edge. We show that for all γ and Δ, and n large, every n-vertex 3-uniform hypergraph of minimum vertex degree $(5 / 9 + γ) (\begin{matrix} n \\ 2 \end{matrix})$ contains every loose spanning tree T with maximum vertex degree Δ. This bound is asymptotically tight, since some loose trees contain perfect matchings.

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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.