In any bipartite graph, the size of a maximum matching equals the size of a minimum vertex cover. Proved by Denes Koenig, it is a foundational duality result of graph theory, later generalized to general graphs by the Tutte-Berge formula and connected to the max-flow min-cut theorem.
Facts
StatementIn a bipartite graph, the number of edges in a maximum matching equals the number of vertices in a minimum vertex cover. This equality between the maximum matching problem and the minimum vertex cover problem holds for bipartite graphs specifically and does not hold for graphs in general. 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. Konig's Theorem, Graph Theory (Wikipedia)
Wikimedia FoundationLead sectionQuote, Lead section
In the mathematical area of graph theory, Konig's theorem, proved by Denes Konig (1931), describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs.
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