生成有界度超树的dirac型条件

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2023-11-22 DOI:10.1016/j.jctb.2023.11.002

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

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引用次数: 0

摘要

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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Dirac-type conditions for spanning bounded-degree hypertrees

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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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.