Upper Bounds on Turán Densities via Extremal Set Theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913179563458560 |
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| author | Chen, Yaobin Liu, Xizhi Yang, Ningyuan Zhu, Tianming |
| author_facet | Chen, Yaobin Liu, Xizhi Yang, Ningyuan Zhu, Tianming |
| contents | We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Turán densities reduce to classical problems in extremal set theory, including the Erdős--Ko--Rado theorem, $L$-intersecting families, and the Erdős matching problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Upper Bounds on Turán Densities via Extremal Set Theory Chen, Yaobin Liu, Xizhi Yang, Ningyuan Zhu, Tianming Combinatorics We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Turán densities reduce to classical problems in extremal set theory, including the Erdős--Ko--Rado theorem, $L$-intersecting families, and the Erdős matching problem. |
| title | Upper Bounds on Turán Densities via Extremal Set Theory |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2606.02135 |