Open Research Index

The Kőnig–Egerváry Theorem on Matchings and Vertex Covers in Bipartite Graphs

Noah Cohen

Palomar Registrypalomar/PALOMAR-2026-09-02-000010Sep 2, 2026math.COscore 0

A complete machine-checked Lean 4 formalization of the Kőnig–Egerváry Theorem (1931) and Gallai identities (1959). Proves strong min-max duality matchingNumber(G) = vertexCoverNumber(G) for 2-colorable graphs G via Hall's defect matching theorem, and formalizes Gallai's identity independenceNumber(G) + vertexCoverNumber(G) = |V(G)|. To the maintainers' knowledge, the theorem was not found in an exact declaration name, docstring, and type signature search of the pinned Mathlib revision (Mathlib v4.34.0-rc1).

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