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arXiv · 2510.19681

On a refinement of the Ahlswede--Katona Theorem

Jianfeng Hou·Xizhi Liu·Yixiao Zhang
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Abstract

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.

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Jianfeng Hou, Xizhi Liu, Yixiao Zhang. 2026-02-09. On a refinement of the Ahlswede--Katona Theorem. https://arxiv.org/abs/2510.19681

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