Dirac-type conditions for spanning bounded-degree hypertrees

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-22 DOI:10.1016/j.jctb.2023.11.002

Matías Pavez-Signé , Nicolás Sanhueza-Matamala , Maya Stein

引用次数: 0

Abstract

We prove that for fixed k, every k-uniform hypergraph on n vertices and of minimum codegree at least $n / 2 + o (n)$ contains every spanning tight k-tree of bounded vertex degree as a subgraph. This generalises a well-known result of Komlós, Sárközy and Szemerédi for graphs. Our result is asymptotically sharp. We also prove an extension of our result to hypergraphs that satisfy some weak quasirandomness conditions.

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生成有界度超树的dirac型条件

证明了对于固定k，每一个有n个顶点且最小余度至少为n/2+o(n)的k-一致超图包含每一个有界顶点度的生成紧k树作为子图。这推广了一个众所周知的关于图形的Komlós, Sárközy和szemersamedi的结果。我们的结果是渐近尖锐的。我们还证明了对满足弱拟随机条件的超图的推广。

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

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