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Peter Frankl
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Tomasz Łuczak
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Katarzyna Mieczkowska
Keywords:
extremal graph theory, matching, hypergraphs
Abstract
We show that if the largest matching in a $k$-uniform hypergraph $G$ on $n$ vertices has precisely $s$ edges, and $n>2k^2s/\log k$, then $H$ has at most $\binom n k - \binom {n-s} k $ edges and this upper bound is achieved only for hypergraphs in which the set of edges consists of all $k$-subsets which intersect a given set of $s$ vertices.
Author Biographies
Tomasz Łuczak, Adam Mickiewicz University
Faculty of Mathematics and Computer Science,
ul. Umultowska 87,
61-614 Poznań, Poland
Katarzyna Mieczkowska, Adam Mickiewicz University
Faculty of Mathematics and Computer Science,
ul. Umultowska 87,
61-614 Poznań, Poland