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A degree sequence strengthening of the vertex degree threshold for a perfect matching in 3-uniform hypergraphs
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Bowtell, Candida and Hyde, Joseph (2022) A degree sequence strengthening of the vertex degree threshold for a perfect matching in 3-uniform hypergraphs. SIAM Journal on Discrete Mathematics, 36 (2). pp. 1038-1063. doi:10.1137/20M1364825 ISSN 0895-4801.
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Official URL: http://dx.doi.org/10.1137/20M1364825
Abstract
The study of asymptotic minimum degree thresholds that force matchings and tilings in hypergraphs is a lively area of research in combinatorics. A key breakthrough in this area was a result of Hàn, Person, and Schacht [SIAM J. Disc. Math., 23 (2009), pp. 732--748] who proved that the asymptotic minimum vertex degree threshold for a perfect matching in an $n$-vertex $3$-graph is $\left(\frac{5}{9}+o(1)\right)\binom{n}{2}$. In this paper, we improve on this result, giving a family of degree sequence results, all of which imply the result of Hàn, Person and Schacht and additionally allow one-third of the vertices to have degree $\frac{1}{9}\binom{n}{2}$ below this threshold. Furthermore, we show that this result is, in some sense, tight.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Combinatorial analysis , Graph theory , Hypergraphs | |||||||||
| Journal or Publication Title: | SIAM Journal on Discrete Mathematics | |||||||||
| Publisher: | Society for Industrial and Applied Mathematics | |||||||||
| ISSN: | 0895-4801 | |||||||||
| Official Date: | 19 April 2022 | |||||||||
| Dates: |
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| Volume: | 36 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 1038-1063 | |||||||||
| DOI: | 10.1137/20M1364825 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | First Published in SIAM Journal on Discrete Mathematics in 36 (2). 2022., published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 6 July 2022 | |||||||||
| Date of first compliant Open Access: | 6 July 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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