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A bipartite Erdo˝s-Ko-Rado theorem

✍ Scribed by James E. Simpson

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
295 KB
Volume
113
Category
Article
ISSN
0012-365X

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Extending the Erdős–Ko–Rado theorem
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## Abstract Let ${\cal F}$ be a __k__‐uniform hypergraph on __n__ vertices. Suppose that $|F\_{1}\cap \cdots \cap F\_{r}|\ge t$ holds for all $F\_{1},\ldots ,F\_{r}\in {\cal F}$. We prove that the size of ${\cal F}$ is at most ${{n-t}\choose {k-t}}$ if $p= {k \over n}$ satisfies and __n__ is suffi