A stability result for almost perfect matchings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917639679377408 |
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| author | Guo, Mingyang Lu, Hongliang |
| author_facet | Guo, Mingyang Lu, Hongliang |
| contents | Let $n,k,s$ be three integers and $β$ be a sufficiently small positive number such that $k\geq 3$, $0<1/n\ll β\ll 1/k$ and $ks+k\leq n\leq (1+β)ks+k-2$. A $k$-graph is called non-trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non-trivial $k$-graph with $n$ vertices and matching number at most $s$. This result confirms a conjecture proposed by Frankl (On non-trivial families without a perfect matching, \emph{European J. Combin.}, \textbf{84} (2020), 103044) for the case when $s$ is sufficiently large. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stability result for almost perfect matchings Guo, Mingyang Lu, Hongliang Combinatorics 05C70 Let $n,k,s$ be three integers and $β$ be a sufficiently small positive number such that $k\geq 3$, $0<1/n\ll β\ll 1/k$ and $ks+k\leq n\leq (1+β)ks+k-2$. A $k$-graph is called non-trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non-trivial $k$-graph with $n$ vertices and matching number at most $s$. This result confirms a conjecture proposed by Frankl (On non-trivial families without a perfect matching, \emph{European J. Combin.}, \textbf{84} (2020), 103044) for the case when $s$ is sufficiently large. |
| title | A stability result for almost perfect matchings |
| topic | Combinatorics 05C70 |
| url | https://arxiv.org/abs/2404.09720 |