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Embedding loose spanning trees in 3-uniform hypergraphs

Pehova, Yani and Petrova, Kalina (2024) Embedding loose spanning trees in 3-uniform hypergraphs. Journal of Combinatorial Theory, Series B, 168. 47 - 67. ISSN 0095-8956

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Identification Number: 10.1016/j.jctb.2024.04.003


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.

Item Type: Article
Official URL:
Additional Information: © 2024 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 02 May 2024 11:18
Last Modified: 15 Jun 2024 02:15

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