  Let $n,s,k$ be three positive integers such that $1\leq s\leq(n-k+1)/k$ and
let $[n]=\{1,\ldots,n\}$. Let $H$ be a $k$-graph with vertex set
$\{1,\ldots,n\}$, and let $e(H)$ denote the number of edges of $H$. Let
$\nu(H)$ and $\tau(H)$ denote the size of a largest matching and the size of a
minimum vertex cover in $H$, respectively. Define
$A^k_i(n,s):=\{e\in\binom{[n]}{k}:|e\cap[(s+1)i-1]|\geq i\}$ for $2\leq i\leq
k$ and $HM^k_{n,s}:=\big\{e\in\binom{[n]}{k}:e\cap[s-1]\neq\emptyset\big\}
\cup\big\{S\big\}\cup \big\{e\in\binom{[n]}{k}: s\in e, e\cap S\neq
\emptyset\}$, where $S=\{s+1,\ldots,s+k\}$. Frankl and Kupavskii conjectured
that if $\nu(H)\leq s$ and $\tau(H)>s$, then $e(H)\leq
\max\{|A^k_2(n,s)|,\ldots ,|A^k_k(n,s)|,|HM^k_{n,s}|\}$. In this paper, we
prove this conjecture for $k=3$ and sufficiently large $n$.
