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The Partitioned Version of the Erdős—Szekeres Theorem

✍ Scribed by Pór; Valtr

Publisher
Springer
Year
2002
Tongue
English
Weight
334 KB
Volume
28
Category
Article
ISSN
0179-5376

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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