  For a graph G, a hypergraph H is called Berge-G if there is a hypergraph H',
isomorphic to H, containing all vertices of G, so that e is contained in f(e)
for each edge e of G, where f is a bijection between E(G) and E(H'). The set of
all Berge-G hypergraphs is denoted B(G). A hypergraph H is called Berge-G
saturated if it does not contain any subhypergraph from B(G), but adding any
new hyperedge of size at least 2 to H creates such a subhypergraph. Each
Berge-G saturated hypergraph has at least |E(G)|-1 hyperedges. We show that for
each graph G that is not a certain star and for any n at least |V(G)|, there is
a Berge-G saturated hypergraph on n vertices and exactly |E(G)|-1 hyperedges.
This solves a problem of finding a saturated hypergraph on n vertices with the
smallest number of edges exactly.
