Extensions of Gallai's graph covering theorems for uniform hypergraphs

AbstractLet H be an r-uniform hypergraph in which the minimum number of edges covering all vertices is ϱ = ϱ(H). In answering two questions of T. Gallai we prove that 1.(1) every collection M of pairwise disjopint edges (=matching) of H is contained in a covering of size at most (2 − r−1)ϱ, and2.(2) every maximum matching M of H is contained in a covering of size at most (2 − (r − 1)−1)ϱ. Both estimates are sharp