A note on hypergraph extensions of Mantel's theorem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916743607222272 |
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| author | Ma, Jie Zhu, Tianming |
| author_facet | Ma, Jie Zhu, Tianming |
| contents | Chao and Yu introduced an entropy method for hypergraph Turán problems, and used it to show that the family of $\lfloor k/2\rfloor$ $k$-uniform tents have Turán density $k!/k^k$. Il'kovič and Yan improved this by reducing to a subfamily of $\lceil k/e\rceil$ tents. In this note, enhancing Il'kovič-Yan's result, we give a significantly shorter entropy proof, with optimal bounds within this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on hypergraph extensions of Mantel's theorem Ma, Jie Zhu, Tianming Combinatorics Chao and Yu introduced an entropy method for hypergraph Turán problems, and used it to show that the family of $\lfloor k/2\rfloor$ $k$-uniform tents have Turán density $k!/k^k$. Il'kovič and Yan improved this by reducing to a subfamily of $\lceil k/e\rceil$ tents. In this note, enhancing Il'kovič-Yan's result, we give a significantly shorter entropy proof, with optimal bounds within this framework. |
| title | A note on hypergraph extensions of Mantel's theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.11373 |