On a refinement of the Ahlswede--Katona Theorem
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917258462232576 |
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| author | Hou, Jianfeng Liu, Xizhi Zhang, Yixiao |
| author_facet | Hou, Jianfeng Liu, Xizhi Zhang, Yixiao |
| contents | A classical theorem of Ahlswede and Katona determines the maximum density of the $2$-edge star in a graph with a given edge density. Motivated by its application in hypergraph Turán problems, we establish a refinement of their result under the additional assumption that the graph contains a large independent set in which every vertex has high degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a refinement of the Ahlswede--Katona Theorem Hou, Jianfeng Liu, Xizhi Zhang, Yixiao Combinatorics A classical theorem of Ahlswede and Katona determines the maximum density of the $2$-edge star in a graph with a given edge density. Motivated by its application in hypergraph Turán problems, we establish a refinement of their result under the additional assumption that the graph contains a large independent set in which every vertex has high degree. |
| title | On a refinement of the Ahlswede--Katona Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.19681 |