On a refinement of the Ahlswede--Katona Theorem
Combinatorics
2026-02-10 v2
Abstract
A classical theorem of Ahlswede and Katona determines the maximum density of the -edge star in a graph with a given edge density. Motivated by its application in hypergraph Tur\'{a}n 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.
Keywords
Cite
@article{arxiv.2510.19681,
title = {On a refinement of the Ahlswede--Katona Theorem},
author = {Jianfeng Hou and Xizhi Liu and Yixiao Zhang},
journal= {arXiv preprint arXiv:2510.19681},
year = {2026}
}
Comments
26 pages, comments are welcome