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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Abstract
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 |
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Official URL: | https://www.sciencedirect.com/journal/journal-of-c... |
Additional Information: | © 2024 The Authors |
Divisions: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Date Deposited: | 02 May 2024 11:18 |
Last Modified: | 01 Dec 2024 06:18 |
URI: | http://eprints.lse.ac.uk/id/eprint/122872 |
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