# networkx.algorithms.approximation.matching.min_maximal_matching¶

min_maximal_matching(G)[source]

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)