Abstract: | Given a graph , a hypergraph is a Berge- if it can be obtained by expanding each edge in to a hyperedge containing it. A hypergraph is Berge--saturated if does not contain a subhypergraph that is a Berge-, but for any edge , does. The -uniform saturation number of Berge- is the minimum number of edges in a -uniform Berge--saturated hypergraph on vertices. For 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 -uniform hypergraphs. |