Positive codegree thresholds for perfect matchings in hypergraphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912389683740672 |
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| author | Mycroft, Richard Zárate-Guerén, Camila |
| author_facet | Mycroft, Richard Zárate-Guerén, Camila |
| contents | We give, for each $k \geq 3$, the precise best possible minimum positive codegree condition for a perfect matching in a large $k$-uniform hypergraph $H$ on $n$ vertices. Specifically we show that, if $n$ is sufficiently large and divisible by $k$, and $H$ has minimum positive codegree $δ^+(H) \geq \frac{k-1}{k}n - (k-2)$ and no isolated vertices, then $H$ contains a perfect matching. For $k=3$ this was previously established by Halfpap and Magnan, who also gave bounds for $k \geq 4$ which were tight up to an additive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive codegree thresholds for perfect matchings in hypergraphs Mycroft, Richard Zárate-Guerén, Camila Combinatorics We give, for each $k \geq 3$, the precise best possible minimum positive codegree condition for a perfect matching in a large $k$-uniform hypergraph $H$ on $n$ vertices. Specifically we show that, if $n$ is sufficiently large and divisible by $k$, and $H$ has minimum positive codegree $δ^+(H) \geq \frac{k-1}{k}n - (k-2)$ and no isolated vertices, then $H$ contains a perfect matching. For $k=3$ this was previously established by Halfpap and Magnan, who also gave bounds for $k \geq 4$ which were tight up to an additive constant. |
| title | Positive codegree thresholds for perfect matchings in hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.17981 |