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...

case of the duality theorem for linear programs and can be used to derive Menger's theorem and the Kőnig–Egerváry theorem. The theorem equates two quantities:...

credited with Menger's theorem. Outside of mathematics, Menger has substantial contributions to game theory and social sciences. Karl Menger was a student...

analogously. One of the most important facts about connectivity in graphs is Menger's theorem, which characterizes the connectivity and edge-connectivity of a graph...

Karl Menger made a further discovery after the development of the Cayley–Menger determinant, which became known as Menger's Theorem. The theorem states:...

König's theorem Menger's theorem (1927) The max-flow min-cut theorem (Ford–Fulkerson algorithm) The Birkhoff–Von Neumann theorem (1946) Dilworth's theorem. In...

ISBN 978-0-8247-8643-4. OCLC 24909067. Tao, Terence, The Hahn–Banach theorem, Menger's theorem, and Helly's theorem Trèves, François (2006) [1967]. Topological Vector Spaces...

matroid by Hazel Perfect (1968), based on considerations related to Menger's theorem characterizing the obstacles to the existence of systems of disjoint...

subspaces of the Euclidean spaces, with their usual topology. The Menger–Nöbeling theorem (1932) states that if X {\displaystyle X} is compact metric separable...

to find k vertex-independent paths connecting these vertices; see Menger's theorem (Diestel 2005, p. 55). This definition produces the same answer, n − 1...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

MacMahon Master theorem (enumerative combinatorics) Menger's theorem (graph theory) Milliken–Taylor theorem (Ramsey theory) Milliken's tree theorem (Ramsey theory)...

can also be found within a Menger sponge. The Menger sponge is a closed set; since it is also bounded, the Heine–Borel theorem implies that it is compact...

San Antonio Texas Menger sponge, a fractal curve Menger's theorem Menger–Urysohn dimension; see Inductive dimension Cayley–Menger determinant; see Distance...

corollary of the Nash-Williams theorem, every 2k-edge connected graph is k-arboric. Both Nash-Williams' theorem and Menger's theorem characterize when a graph...

MR 2083752, S2CID 119615076. Aharoni, Ron; Berger, Eli (2009), "Menger's Theorem for infinite graphs", Inventiones Mathematicae, 176 (1): 1–62, arXiv:math/0509397...

This page is a list of network theory topics. Max flow min cut theorem Menger's theorem Metcalfe's law Centrality Betweenness centrality Closeness Bose-Einstein...

\tau (H)} is the size of the smallest edge-cut separating s and t, so Menger's theorem (edge-connectivity version) asserts that ν ( H ) = τ ( H ) {\displaystyle...

proved by Karl Menger in 1930. Since then, several new proofs of the theorem have been discovered. In the Soviet Union, Kuratowski's theorem was known as...

number) Lise Meitner, physicist Karl Menger, mathematician (Menger's theorem, Menger sponge); son of Carl Menger) Ronald Micura, chemist Richard von Mises...

 631–638. doi:10.1145/1536414.1536500. Aharoni, Ron; Berger, Eli (2009). "Menger's theorem for infinite graphs". Inventiones Mathematicae. 176 (1): 1–62. arXiv:math/0509397...

well-balanced orientations, together with Menger's theorem, immediately implies Robbins' theorem: by Menger's theorem, a 2-edge-connected graph has at least...

be connected by vertex-disjoint paths within the disk, by a form of Menger's theorem for planar graphs. However, the total length of these paths would necessarily...

starting with Menger's theorem, guarantee the existence of paths or cycles in a k-connected graph. For 2-connected graphs, Menger's theorem is equivalent...

defining the ends of infinite graphs, for Halin's grid theorem, for extending Menger's theorem to infinite graphs, and for his early research on treewidth...

of a given graph in discrete mathematics. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally...

He subsequently proved the appropriate versions of the Kőnig theorem and the Menger theorem for infinite graphs (the latter with Eli Berger). Aharoni is...

doi:10.21136/CMJ.1976.101409. Zelinka, Bohdan (1976b), "Analoga of Menger's theorem for polar and polarized graphs", Czechoslovak Mathematical Journal...

disconnects G is a minimum cut in G. The edge connectivity version of Menger's theorem provides an alternative and equivalent characterization, in terms of...

from the observation that the Cayley–Menger determinant of the four coplanar circle centers is zero. Descartes' theorem is most easily stated in terms of...