A Formal Correctness Proof of Edmonds’ Blossom Shrinking Algorithm
Abstract
Abstract We present the first formal correctness proof of Edmonds’ blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and properties that allow the algorithm to run in worst-case polynomial running time. We formalise Berge’s lemma, blossoms and their properties, and a mathematical model of the algorithm, showing that it is totally correct. We provide the first detailed proofs of many of the facts underlying the algorithm’s correctness.
Fields of Study & Subjects
Logic
programming
and type systems
Complexity and Algorithms in Graphs
Formal Methods in Verification
Publication details
- Journal / source
- Journal of Automated Reasoning
- Volume
- 70
- Issue
- 1
- Publication date
- 16 February 2026
- Language
- EN