Extending the Erdős–Ko–Rado theorem

✍ Scribed by Norihide Tokushige

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 75 KB
• Volume: 14
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20085

✦ Synopsis

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 sufficiently large. © 2005 Wiley Periodicals, Inc. J Combin Designs