# General Graph MCM (Maximum Cardinality Matching)

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## Description

The goal of maximum cardinality matching is to find a matching with as many edges as possible (equivalently: a matching that covers as many vertices as possible). Here, the graph can be any general graph.

## Related Problems

Subproblem: Bipartite Graph MCM

Related: Planar Bipartite Graph Perfect Matching

## Parameters

$V$: number of vertices

$E$: number of edges

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Micali and Vazirani | 1980 | $O(V^{0.5} E)$ | $O(V)$ | Deterministic | Time & Space | |

Blum | 1990 | $O((V^{0.5})$E) | $O(E)$?? | Exact | Deterministic | Time |

Gabow; Tarjan | 1991 | $O((V^{0.5})$E) | $O(E)$? | Exact | Deterministic | Time & Space |

Mucha, Sankowski (general) | 2004 | $O(V^{2.{37}6})$ | $O(V^{2})$?? | Exact | Randomized | Time |