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networkx.algorithms.approximation.matching.min_maximal_matching

min_maximal_matching(G)

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 – 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. Return type:set

Notes

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 \(O(|E|)\).

References

[1]	Vazirani, Vijay Approximation Algorithms (2001)