Codegree conditions for (fractional) Steiner triple systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910019457384448 |
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| author | Zheng, Michael |
| author_facet | Zheng, Michael |
| contents | We establish an upper bound on the minimum codegree necessary for the existence of spanning, fractional Steiner triple systems in $3$-uniform hypergraphs. This improves upon a result by Lee in 2023. In particular, together with results from Lee's paper, our results imply that if $n$ is sufficiently large and satisfies some necessary divisibility conditions, then a $3$-uniform, $n$-vertex hypergraph $H$ contains a Steiner triple system if every pair of vertices forms an edge in $H$ with at least $0.8579n$ other vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codegree conditions for (fractional) Steiner triple systems Zheng, Michael Combinatorics We establish an upper bound on the minimum codegree necessary for the existence of spanning, fractional Steiner triple systems in $3$-uniform hypergraphs. This improves upon a result by Lee in 2023. In particular, together with results from Lee's paper, our results imply that if $n$ is sufficiently large and satisfies some necessary divisibility conditions, then a $3$-uniform, $n$-vertex hypergraph $H$ contains a Steiner triple system if every pair of vertices forms an edge in $H$ with at least $0.8579n$ other vertices. |
| title | Codegree conditions for (fractional) Steiner triple systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.07981 |