Maximum Cardinality Matching in $n^{2+o(1)}$ Time

We consider the maximum cardinality matching problem in general graphs, and give an $n^{2+o(1)}$-time algorithm for the problem. Our work builds on recent work on combinatorial algorithms for maximum flow and extends the techniques to skew-symmetric flow problems which capture general matchings as a special case.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40591
Primary Topic
Complexity and Algorithms in Graphs
Type
preprint
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preprint

Maximum Cardinality Matching in $n^{2+o(1)}$ Time

George Z. Li, Junkai Zhang, Jason Li
arXiv (Cornell University)
Complexity and Algorithms in Graphs
preprint

Maximum Cardinality Matching in $n^{2+o(1)}$ Time

George Z. Li, Junkai Zhang, Jason Li
preprint en

Abstract

We consider the maximum cardinality matching problem in general graphs, and give an $n^{2+o(1)}$-time algorithm for the problem. Our work builds on recent work on combinatorial algorithms for maximum flow and extends the techniques to skew-symmetric flow problems which capture general matchings as a special case.

arXiv (Cornell University)
Complexity and Algorithms in Graphs
DOIOpen Access PDFOpenAlex
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Maximum Cardinality Matching in $n^{2+o(1)}$ Time — George Z. Li, Junkai Zhang, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS