Tian-Hong Kan

Ore-degree conditions for hypergraph matchings

Let $\sigma_k(H)$ be the minimum sum of the vertex degrees over all non-edges of an $n$-vertex $k$-uniform hypergraph $H$. For every $k\ge3$, $n\geq ks$ and sufficiently large $n$, we establish a sharp Ore-type degree condition that forces a matching of size $s$ in $H$. Specifically, we prove that if \[ \sigma_k(H)>\ma...