On the Matching Problem in Random Hypergraphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918146003173376 |
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| author | Frankl, Peter Nie, Jiaxi Wang, Jian |
| author_facet | Frankl, Peter Nie, Jiaxi Wang, Jian |
| contents | We study a variant of the Erdős Matching Problem in random hypergraphs. Let $\mathcal{K}_p(n,k)$ denote the Erdős-Rényi random $k$-uniform hypergraph on $n$ vertices where each possible edge is included with probability $p$. We show that when $n\gg k^{2}s$ and $p$ is not too small, with high probability, the maximum number of edges in a sub-hypergraph of $\mathcal{K}_p(n,k)$ with matching number $s$ is obtained by the trivial sub-hypergraphs, i.e. the sub-hypergraph consisting of all edges containing at least one vertex in a fixed set of $s$ vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Matching Problem in Random Hypergraphs Frankl, Peter Nie, Jiaxi Wang, Jian Combinatorics 05D05, O5D40 We study a variant of the Erdős Matching Problem in random hypergraphs. Let $\mathcal{K}_p(n,k)$ denote the Erdős-Rényi random $k$-uniform hypergraph on $n$ vertices where each possible edge is included with probability $p$. We show that when $n\gg k^{2}s$ and $p$ is not too small, with high probability, the maximum number of edges in a sub-hypergraph of $\mathcal{K}_p(n,k)$ with matching number $s$ is obtained by the trivial sub-hypergraphs, i.e. the sub-hypergraph consisting of all edges containing at least one vertex in a fixed set of $s$ vertices. |
| title | On the Matching Problem in Random Hypergraphs |
| topic | Combinatorics 05D05, O5D40 |
| url | https://arxiv.org/abs/2410.15585 |