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A linear upper bound for Berge saturation numbers
For a graph $F$ with at least one edge, a $k$-uniform hypergraph is Berge-$F$-saturated if it contains no Berge-$F$, but adding any missing hyperedge creates a Berge-$F$. The saturation number $\text{sat}_k(n,\text{Berge-}F)$ is the minimum number of edges in such a hypergraph on $n$ vertices. Engli
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