Exact Turán densities in triple systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909681832689664 |
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| author | Chen, Nannan Qi, Yuzhen Yang, Caihong Zhao, Hongbin |
| author_facet | Chen, Nannan Qi, Yuzhen Yang, Caihong Zhao, Hongbin |
| contents | In this paper, we prove several new Turán density results for $3$-graphs. We show: $π(C_4^3, \mathrm{complement\ of\ } F_5) = 2\sqrt{3} - 3$, $π(F_{3,2}, C_5^{3-}) = \frac{2}{9}$, and $π(F_{3,2}, \mathrm{induced\ complement\ of\ } F_{3,2}) = \frac{3}{8}$. The first result confirms the conjecture of Shi~[On Turán denisties of small triple graphs, European J. Combin. 52 (2016) 95-102]. The other results give several special non-principal family posed by Mubayi and Rödl~[On the Turán number of triple systems, J. Combin. Theory A. 100 (2002) 135-152]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Turán densities in triple systems Chen, Nannan Qi, Yuzhen Yang, Caihong Zhao, Hongbin Combinatorics In this paper, we prove several new Turán density results for $3$-graphs. We show: $π(C_4^3, \mathrm{complement\ of\ } F_5) = 2\sqrt{3} - 3$, $π(F_{3,2}, C_5^{3-}) = \frac{2}{9}$, and $π(F_{3,2}, \mathrm{induced\ complement\ of\ } F_{3,2}) = \frac{3}{8}$. The first result confirms the conjecture of Shi~[On Turán denisties of small triple graphs, European J. Combin. 52 (2016) 95-102]. The other results give several special non-principal family posed by Mubayi and Rödl~[On the Turán number of triple systems, J. Combin. Theory A. 100 (2002) 135-152]. |
| title | Exact Turán densities in triple systems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.07360 |