Results and Open Problems on Minimum Saturated Hypergraphs

Abstract

Let \(\mathcal{F}\) be a family of \(k\)-graphs. A \(k\)-graph \(G\) is called \(\mathcal{F}\)-saturated if it is a maximal graph not containing any member of \(\mathcal{F}\) as a subgraph. We investigate the smallest number of edges that an \(\mathcal{F}\)-saturated graph on \(n\) vertices can have. We present new results and open problems for different instances of \(\mathcal{F}\).