Maximum matching by Edmonds
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Abstract view
Invariant: The current selection [math]\displaystyle{ M }[/math] of edges is a matching.
Variant: Either the cardinality of [math]\displaystyle{ M }[/math] increases, or the number of nodes of [math]\displaystyle{ G }[/math] decreases.
Break condition: There is no more augmenting path.
Induction basis
Abstract view: Start with some matching, for example, the empty matching.
Proof: Obvious.