Saturation of Berge hypergraphs

Given a graph F, a hypergraph is a Berge-F if it can be obtained by expanding each edge in F to a hyperedge containing it. A hypergraph H is Berge-F-saturated if H does not contain a subhypergraph that is a Berge-F, but for any edge e is an element of E((H) over bar), H + e does. The k-uniform saturation number of Berge-F is the minimum number of edges in a k-uniform Berge-F-saturated hypergraph on n vertices. For k = 2 this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in k-uniform hypergraphs. (C) 2019 Elsevier B.V. All rights reserved.