A Survey of Minimum Saturated Graphs

Jill R. Faudree, Ralph J. Faudree, John R. Schmitt

Abstract


Given a family of (hyper)graphs $\mathcal{F}$ a (hyper)graph $G$ is said to be $\mathcal{F}$-saturated if $G$ is $F$-free for any $F \in\mathcal{F}$ but for any edge e in the complement of $G$ the (hyper)graph $G + e$ contains some $F\in\mathcal{F}$. We survey the problem of determining the minimum size of an $\mathcal{F}$-saturated (hyper)graph and collect many open problems and conjectures.


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