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<p>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.</p>

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A Formal Correctness Proof of Edmonds’ Blossom Shrinking Algorithm

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月16日

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  • Mohammad Abdulaziz,
  • Kurt Mehlhorn

摘要

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.