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Returns the minimum maximal matching of G. That is, out of all maximal matchings of the graph G, the smallest is returned.

Parameters :

G : NetworkX graph

Undirected graph

Returns :

min_maximal_matching : set

Returns a set of edges such that no two edges share a common endpoint and every edge not in the set shares some common endpoint in the set. Cardinality will be 2*OPT in the worst case.


The algorithm computes an approximate solution fo the minimum maximal cardinality matching problem. The solution is no more than 2 * OPT in size. Runtime is \(O(|E|)\).


[R143]Vazirani, Vijay Approximation Algorithms (2001)