English

A Proof of the MV Matching Algorithm

Data Structures and Algorithms 2020-12-08 v1 Combinatorics

Abstract

The Micali-Vazirani (MV) algorithm for maximum cardinality matching in general graphs, which was published in 1980 \cite{MV}, remains to this day the most efficient known algorithm for the problem. This paper gives the first complete and correct proof of this algorithm. Central to our proof are some purely graph-theoretic facts, capturing properties of minimum length alternating paths; these may be of independent interest. An attempt is made to render the algorithm easier to comprehend.

Cite

@article{arxiv.2012.03582,
  title  = {A Proof of the MV Matching Algorithm},
  author = {Vijay V. Vazirani},
  journal= {arXiv preprint arXiv:2012.03582},
  year   = {2020}
}

Comments

43 pages. arXiv admin note: text overlap with arXiv:1210.4594

R2 v1 2026-06-23T20:46:34.789Z