Let F be a family of forbidden k-hypergraphs (k-uniform set systems). An F-saturated hypergraph is a maximal k-uniform set system not containing any member of F. As the main result we prove that, for any finite family F, the minimum number of edges of an F-saturated hypergraph is O(nk−1). In particular, this implies a conjecture of Tuza. Some other related results are presented.
['Oleg Pikhurko']
The Minimum Size of Saturated Hypergraphs