On Matchings in Hypergraphs

Peter Frankl, Tomasz Łuczak, Katarzyna Mieczkowska

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.

Keywords


extremal graph theory, matching, hypergraphs

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