在 3-Uniform 超图中嵌入松散生成树

IF 1.2 1区 数学 Q1 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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)(n2) 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
CiteScore
2.70
自引率
14.30%
发文量
99
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.
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