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Tutte theorem information


Example of a graph and one of its perfect matchings (in red).

In the mathematical discipline of graph theory the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings. It is a generalization of Hall's marriage theorem from bipartite to arbitrary graphs.[clarification needed] It is a special case of the Tutte–Berge formula.

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Tutte theorem

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In the mathematical discipline of graph theory the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs...

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Planar graph

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eigenvalue of certain Schrödinger operators defined by the graph. The Hanani–Tutte theorem states that a graph is planar if and only if it has a drawing in which...

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BEST theorem

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discovered it: N. G. de Bruijn, Tatyana Ehrenfest, Cedric Smith and W. T. Tutte. Let G = (V, E) be a directed graph. An Eulerian circuit is a directed closed...

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Tutte homotopy theorem

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In mathematics, the Tutte homotopy theorem, introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly...

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Perfect matching

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factor-critical. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching. The Tutte theorem provides a characterization...

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Tatyana Ehrenfest

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larger alphabets, in 1951.[3] The BEST theorem, also known as the de Bruijn–van Aardenne-Ehrenfest–Smith–Tutte theorem, relates Euler tours and spanning trees...

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List of theorems

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Tunnell's theorem (number theory) Tutte theorem (graph theory) Turán's theorem (graph theory) Turán–Kubilius theorem (number theory) Tverberg's theorem (discrete...

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Tutte embedding

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equations geometrically produces a planar embedding. Tutte's spring theorem, proven by W. T. Tutte (1963), states that this unique solution is always crossing-free...

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Hamiltonian path

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(1931), "A theorem on graphs", Annals of Mathematics, Second Series, 32 (2): 378–390, doi:10.2307/1968197, JSTOR 1968197, MR 1503003 Tutte, W. T. (1956)...

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Tutte polynomial

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The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

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Graph coloring

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triangle, and the example can be generalized to the Mycielskians. Theorem (William T. Tutte 1947, Alexander Zykov 1949, Jan Mycielski 1955): There exist triangle-free...

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Tutte graph

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later, in many cases based on Grinberg's theorem. From a small planar graph called the Tutte fragment, W. T. Tutte constructed a non-Hamiltonian polyhedron...

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Matroid

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theorem the theory of chain groups and their matroids and the tools he used to prove many of his results: the "Path theorem" "Tutte homotopy theorem"...

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List of things named after Alexander Grothendieck

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(1928–2014) is the eponym of many things. Ax–Grothendieck theorem Birkhoff–Grothendieck theorem Brieskorn–Grothendieck resolution Dolbeault-Grothendieck...

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