Huang–Zhao matching conjecture for minimum vertex degree

Let $H$ be a $k$-graph on $n$ vertices, let $\delta_1(H)$ denote its minimum vertex degree, and let $\nu(H)$ denote the maximum size of a matching in $H$.

Huang–Zhao conjecture. For positive integers $m,k,n$ satisfying $m<n/k$, if

$$\delta_1(H)>\binom{n-1}{k-1}-\binom{n-m}{k-1},$$

then

$$\nu(H)\geq m.$$

This conjecture strengthens the cited theorem of Huang and Zhao by replacing the hypothesis $n\geq 3k^2m$ with the natural range $m<n/k$. It concerns sharp minimum vertex-degree conditions forcing a matching of prescribed size and remains open in the source.