Extensions of Gallai's graph covering theorems for uniform hypergraphs (Q1179466)

Let \(H\) be an \(r\)-uniform hypergraph in which the minimum number of edges covering all vertices is \(p\). It is proved that every matching of \(H\) is contained in a covering of size at most \((2-r^{-1})p\) and every maximum matching of \(H\) is contained in a covering of size at most \((2-(r-1)^{- 1})p\).