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Hypergraphs and Sperner's theorem

✍ Scribed by B. Monjardet


Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
237 KB
Volume
5
Category
Article
ISSN
0012-365X

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One of the best-known results of extremal combinatorics is Sperner's theorem, which asserts that the maximum size of an antichain of subsets of an n-element set equals the binomial coefficient n n/2 , that is, the maximum of the binomial coefficients. In the last twenty years, Sperner's theorem has

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A classical theorem of Claude Shannon states that for any multigraph G without loops, Ο‡ (G) ≀ 3 2 (G) . We suggest a generalization of Shannon's theorem to hypergraphs and prove it in case of hypergraphs without repeated edges of size 2.