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Menger's theorem

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. Proved by Karl Menger in 1927, it characterizes the connectivity of a graph. It is generalized by the max-flow min-cut theorem, which…

Infinite graphs, Other proofs & Edge connectivity

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Infinite graphs

EndsHalin 1974Ron AharoniEli BergerPaul Erdős
5 related topics

Other proofs

Linear programsDigraphKőnig's theoremBipartite graph
4 related topics

Edge connectivity

Edge cutEdge-disjoint pathsK-edge-connected
3 related topics

Vertex connectivity

NonadjacentVertex cutK-vertex-connected
3 related topics

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Edge connectivity

Vertex connectivity

Other proofs

Infinite graphs

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Menger's theorem

Nodes31
Edges30
Triples35
Avg. degree1.94
Density0.064516
Components1

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Menger's theorem

Top relations

related to Further reading · 19
Menger's theorem → Abhandlungen, Aharoni, Berger, BF02993589, Bibcode, Eli, Fund, Halin, Inventiones Mathematicae, Karl, Kurventheorie, Math, Mathematischen Seminar, Menger, Menger's, Ron, S2CID, Universität Hamburg, Zur
related to Infinite graphs · 9
Menger's theorem → Eli Berger, Erdős, Halin, It, Menger, Menger's, Paul Erdős, Ron Aharoni, The
related to External links · 3
Menger's theorem → Max-Flow-Min-Cut, Menger's TheoremMenger's Theorems, Proof
related to Edge connectivity · 2
Menger's theorem → Menger's, The
related to Vertex connectivity · 2
Menger's theorem → Menger's, The

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theorem size vertices graph edge vertex ab-separator menger's paths directed edges version graphs path minimum set also ab-path ab-connector every

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Menger's theoremrelated to Edge connectivityThe0.60section
Menger's theoremrelated to Edge connectivityMenger's0.60section
Menger's theoremrelated to External linksProof0.60section
Menger's theoremrelated to External linksMenger's TheoremMenger's Theorems0.60section
Menger's theoremrelated to External linksMax-Flow-Min-Cut0.60section
Menger's theoremrelated to Further readingMenger0.60section
Menger's theoremrelated to Further readingKarl0.60section
Menger's theoremrelated to Further readingZur0.60section
Menger's theoremrelated to Further readingKurventheorie0.60section
Menger's theoremrelated to Further readingFund0.60section
Menger's theoremrelated to Further readingMath0.60section
Menger's theoremrelated to Further readingAharoni0.60section

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