Appendix: on edge–isoperimetric theorems for uniform hypergraphs

  • Authors:

  • R. Ahlswede;N. Cai

  • Affiliations:

  • Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany;Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany

  • Venue:
  • General Theory of Information Transfer and Combinatorics
  • Year:
  • 2006

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Abstract

Denote by Ω={1,...,n} an n–element set. For all $A,B\in\binom{\Omega}k$, the k–element subsets of Ω, define the relation ~ as follows: A~B iff A and B have a common shadow, i.e. there is a $C\in\binom{\Omega}{k-1}$ with C ⊂A and C ⊂B. For fixed integer α, our goal is to find a family ${\mathcal A}$ of k–subsets with size α, having as many as possible ~–relations for all pairs of its elements. For k=2 this was achieved by Ahlswede and Katona [2] many years ago.