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Saturation (graph theory)

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Given a graph , another graph is -saturated if does not contain a (not necessarily induced) copy of , but adding any edge to it does. The function is the minimum number of edges an -saturated graph on vertices can have.[1]

In matching theory, there is a different definition. Let be a graph and a matching in . A vertex is said to be saturated by if there is an edge in incident to . A vertex with no such edge is said to be unsaturated by . We also say that saturates .

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