id: 06042688
dt: j
an: 06042688
au: Huang, Hao; Loh, Po-Shen; Sudakov, Benny
ti: The size of a hypergraph and its matching number.
so: Comb. Probab. Comput. 21, No. 3, 442-450 (2012).
py: 2012
pu: Cambridge University Press, Cambridge
la: EN
cc: 
ut: 
ci: 
li: doi:10.1017/S096354831100068X
ab: Summary: More than forty years ago, Erdős conjectured that for any , every
    $k$-uniform hypergraph on $n$ vertices without $t$ disjoint edges has
    at most max $\lbrace {{kt-1} \choose k}, {n \choose k}-{{n-t+1} \choose
    k}\rbrace $ edges. Although this appears to be a basic instance of the
    hypergraph Turán problem (with a $t$-edge matching as the excluded
    hypergraph), progress on this question has remained elusive. In this
    paper, we verify this conjecture for all $t<\frac{n}{3k^{2}}$. This
    improves upon the best previously known range $t=O(\frac{n}{k^{3}})$,
    which dates back to the 1970s.
rv: