[isabelle] New AFP entry: Maximum Cardinality Matching

Maximum Cardinality Matching
Christine Rizkallah

A matching in a graph G is a subset M of the edges of G such that no two
share an endpoint. A matching has maximum cardinality if its cardinality
is at least as large as that of any other matching. An odd-set cover OSC
of a graph G is a labeling of the nodes of G with integers such that
every edge of G is either incident to a node labeled 1 or connects two
nodes labeled with the same number i ≥ 2. This article proves Edmonds
theorem: Let M be a matching in a graph G and let OSC be an odd-set
cover of G. For any i ≥ 0, let n(i) be the number of nodes labeled i. If
|M| = n(1) + ∑i ≥ 2(n(i) div 2), then M is a maximum cardinality matching.


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