A note on Huang-Zhao theorem on intersecting families with large minimum degree

Using the linear algebra method Huang and Zhao proved that if n>2k and F is an intersecting n-vertex k-uniform hypergraph with minimum degree at least n−2k−2, then F is the star. In this note we present an elementary, combinatorial proof of this result for the case n≥3k. We also prove a vector space version of the Huang-Zhao result along the same line as their proof.