Saturation (graph theory)

Given a graph $$H$$, another graph $$G$$ is $$H$$-saturated if $$G$$ does not contain a (not necessarily induced) copy of $$H$$, but adding any edge to $$G$$ it does. The function $$sat(n,H)$$ is the minimum number of edges an $$H$$-saturated graph $$G$$ on $$n$$ vertices can have.

In matching theory, there is a different definition. Let $$G(V,E)$$ be a graph and $$M$$ a matching in $$G$$. A vertex $$v\in V(G)$$ is said to be saturated by $$M$$ if there is an edge in $$M$$ incident to $$v$$. A vertex $$v\in V(G)$$ with no such edge is said to be unsaturated by $$M$$. We also say that $$M$$ saturates $$v$$.