On a refinement of the Ahlswede--Katona Theorem
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 Tur\'an 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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