Geodesic
On the VC-dimension of uniform hypergraphs
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 1, pp. 101-110.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $F {\cal F}$ be a $k$-uniform hypergraph on $[ n]$ where $k - 1$ is a power of some prime $p$ and $n\geq n _{0}( k)$. Our main result says that if $|F|> ({n\atop k-1}) -\log_p n + k!k^k $ |F|> (n$\atop $k-1) -$\log_p n + k$!k^k , then there exists $E _{0}\epsilon F {\cal F}$ such that ${ E\cap E _{0}: E\epsilon F {\cal F}}$ contains all subsets of $E _{0}$. This improves a longstanding bound of ([$( n) || ( k -1)$]) (n$\atop $k-1) due to Frankl and Pach [7].
Keywords: keywords trace, hypergraph, VC-dimension, extremal problems 
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Mubayi, Dhruv; Zhao, Yi. On the VC-dimension of uniform hypergraphs. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/JAC_2007__25_1_a0/