  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 subgraph that is a Berge-$F$, but
for any edge $e\in E(\overline{H})$, $H+e$ 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.
