  Let $F$ be a graph and $\mathcal{H}$ be a hypergraph, both embedded on the
same vertex set. We say $\mathcal{H}$ is a Berge-$F$ if there exists a
bijection $\phi:E(F)\to E(\mathcal{H})$ such that $e\subseteq \phi(e)$ for all
$e\in E(F)$. We say $\mathcal{H}$ is Berge-$F$-saturated if $\mathcal{H}$ does
not contain any Berge-$F$, but adding any missing edge to $\mathcal{H}$ creates
a copy of a Berge-$F$.
  The saturation number $\mathrm{sat}_k(n,\text{Berge-}F)$ is the least number
of edges in a Berge-$F$-saturated $k$-uniform hypergraph on $n$ vertices.
  We show
  \[
  \mathrm{sat}_k(n,\text{Berge-}K_\ell)\sim \frac{\ell-2}{k-1}n,
  \]
  for all $k,\ell\geq 3$. Furthermore, we provide some sufficient conditions to
imply that $\mathrm{sat}_k(n,\text{Berge-}F)=O(n)$ for general graphs $F$.
