# Appendix: On Edge-Isoperimetric Theorems for Uniform Hypergraphs

• Published 2006 in GTIT-C

#### Abstract

Denote by Ω = {1, . . . , n} an n–element set. For all A,B ∈ Ωk ) , 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 ∈ ( Ω k−1 ) with C ⊂ A and C ⊂ B. For fixed integer α, our goal is to find a family 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. However,

DOI: 10.1007/11889342_63

### Cite this paper

@inproceedings{Ahlswede2006AppendixOE, title={Appendix: On Edge-Isoperimetric Theorems for Uniform Hypergraphs}, author={Rudolf Ahlswede and Ning Cai}, booktitle={GTIT-C}, year={2006} }