On a Refinement of the Ahlswede-Katona Theorem
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.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Topological and Geometric Data Analysis
Geometric and Algebraic Topology
Publication details
- Journal / source
- Annals of Applied Mathematics
- Publisher
- Global Science Press
- Volume
- 42
- Issue
- 1
- Pages
- 1–32
- Publication date
- 23 July 2026