In a finite graph, the maximum number of pairwise vertex-disjoint paths between two non-adjacent vertices equals the minimum number of vertices whose removal disconnects them. Proved by Karl Menger, it is a foundational connectivity result of graph theory, later shown to be a special case of the max-flow min-cut theorem.
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StatementIn the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices. 2 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.
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1. Wikipedia: Menger's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices.
2. Menger's Theorem (Wikipedia)
Wikimedia FoundationLead section, first sentence
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found between any pair of vertices.
Lead section, second sentence
Proved by Karl Menger in 1927, it characterizes the connectivity of a graph.
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