Editing Matching (graph theory) (section)

=== Maximum-cardinality matching ===
{{Main|Maximum cardinality matching}}
A fundamental problem in [[combinatorial optimization]] is finding a ''maximum matching''. This problem has various algorithms for different classes of graphs.

In an ''unweighted bipartite graph'', the optimization problem is to find a [[maximum cardinality matching]].  The problem is solved by the [[Hopcroft-Karp algorithm]] in time {{math|<var>O</var>({{radical|<var>V</var>}}<var>E</var>)}} time, and there are more efficient [[randomized algorithm]]s, [[approximation algorithm]]s, and algorithms for special classes of graphs such as bipartite [[planar graph]]s, as described in the main article.