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.
@article{10_37236_2176,
author = {Peter Frankl and Tomasz {\L}uczak and Katarzyna Mieczkowska},
title = {On matchings in hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {2},
doi = {10.37236/2176},
zbl = {1252.05092},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2176/}
}
TY - JOUR
AU - Peter Frankl
AU - Tomasz Łuczak
AU - Katarzyna Mieczkowska
TI - On matchings in hypergraphs
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2176/
DO - 10.37236/2176
ID - 10_37236_2176
ER -
%0 Journal Article
%A Peter Frankl
%A Tomasz Łuczak
%A Katarzyna Mieczkowska
%T On matchings in hypergraphs
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2176/
%R 10.37236/2176
%F 10_37236_2176
Peter Frankl; Tomasz Łuczak; Katarzyna Mieczkowska. On matchings in hypergraphs. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2176
