When entropy meets Turán: new proofs and hypergraph Turán results
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912812685590528 |
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| author | Chao, Ting-Wei Yu, Hung-Hsun Hans |
| author_facet | Chao, Ting-Wei Yu, Hung-Hsun Hans |
| contents | In this paper, we provide a new proof of a density version of Turán's theorem. We also rephrase both the theorem and the proof using entropy. With the entropic formulation, we show that some naturally defined entropic quantity is closely connected to other common quantities such as Lagrangian and spectral radius. In addition, we also determine the Turán density for a new family of hypergraphs, which we call tents. Our result can be seen as a new generalization of Mubayi's result on the extended cliques. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When entropy meets Turán: new proofs and hypergraph Turán results Chao, Ting-Wei Yu, Hung-Hsun Hans Combinatorics 05C35, 05C65, 94A17 In this paper, we provide a new proof of a density version of Turán's theorem. We also rephrase both the theorem and the proof using entropy. With the entropic formulation, we show that some naturally defined entropic quantity is closely connected to other common quantities such as Lagrangian and spectral radius. In addition, we also determine the Turán density for a new family of hypergraphs, which we call tents. Our result can be seen as a new generalization of Mubayi's result on the extended cliques. |
| title | When entropy meets Turán: new proofs and hypergraph Turán results |
| topic | Combinatorics 05C35, 05C65, 94A17 |
| url | https://arxiv.org/abs/2412.08075 |