The Tutte-Berge Formula gives an exact expression for the size of a maximum matching in an arbitrary graph, generalizing Tutte's Theorem on when a graph has a perfect matching to graphs that may not have one, by computing the largest possible matching through a deficiency formula counting the graph's odd components after removing a suitable vertex set. Named for W. T. Tutte, who proved the perfect-matching case, and Claude Berge, who proved the general formula, it is a foundational result of matching theory in graph theory.
Facts
StatementThe size of a maximum matching in a graph equals one half of the minimum, over all vertex subsets U, of the quantity |U| minus the number of odd components of the graph after removing U, plus the total number of vertices. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Tutte-Berge formula (Wikipedia)
Lead paragraph
The Tutte-Berge formula is a characterization of the size of a maximum matching in a graph.
References, Berge 1958 entry
Berge, C. (1958). Sur le couplage maximum d'un graphe. Comptes rendus hebdomadaires des seances de l'Academie des sciences. 247: 258-259.
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