Formal proof demonstrates the correctness of Edmonds' algorithm for maximum matching in graphs, indicating its robustness.
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.
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Abdulaziz et al. (2026) studied this question.
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