maximal matching

A maximal independent edge set of a graph is an independent edge set that cannot be expanded to another independent edge set by addition of any edge in the graph. Note that a maximal independent edge set is not equivalent to a maximum independent edge set, which is an independent edge set containing the largest possible number of edges among all independent edge sets. A maximum independent edge set is always maximal, but the converse does not hold. A maximal independent edge set of a graph can be computed in the Wolfram Language using FindIndependentEdgeSet[g].

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