Explain the difference between a maximal and a maximum matching, with the help of an example.

In graph theory, a matching in a graph is a set of edges without common vertices. Two important concepts related to matchings are maximal matchings and maximum matchings.

A maximal matching in a graph is a matching that cannot be extended by adding an edge while still maintaining the property of being a matching. In other words, adding any more edges ____ __________ ________ _________ _____ ____ __________ ______ __________ ___ ________ ______.
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