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On a Refinement of the Ahlswede-Katona Theorem
Jianfeng Hou, Xizhi Liu, Yixiao Zhang
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Source: Crossref
Published: Jul 23, 2026
DOI: 10.4208/10.4208/aam.oa-2025-0031
Open original source ↗Source abstract
A classical theorem of Ahlswede and Katona [1] 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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