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

mid-1930s. Even though Tutte's contributions to graph theory have been influential to modern graph theory and many of his theorems have been used to keep...

In topological graph theory, the Hanani–Tutte theorem is a result on the parity of edge crossings in a graph drawing. It states that every drawing in...

provided by the Tutte theorem. A generalization of Hall's theorem to bipartite hypergraphs is provided by various Hall-type theorems for hypergraphs....

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...

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...

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

theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte theorem on perfect...

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

odd number of vertices is at most the cardinality of U. Then by the Tutte theorem G contains a perfect matching. Let Gi be a component with an odd number...

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...

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...

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

force Tutte embedding Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595. "Lami's Theorem -...

graphs. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching and the Tutte theorem provides a characterization...

components play a key role in the Tutte theorem characterizing finite graphs that have perfect matchings and the associated Tutte–Berge formula for the size...

can be no Hamiltonian cycle. The resulting Tutte graph is 3-connected and planar, so by Steinitz' theorem it is the graph of a polyhedron. In total it...

type described by Tutte's theorem, may be formed by projecting such a polyhedral representation onto the plane. The Circle packing theorem states that every...

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...

field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees...

two-dimensional Tutte embeddings into three dimensions using the Maxwell–Cremona correspondence, and methods using the circle packing theorem to generate...

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...

(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)...

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...

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"...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests)...

vertices where n is even. Does G contain a perfect matching? Theorem 2 (Tutte 1947): A Tutte matrix determinant is not a 0-polynomial if and only if there...

structure are largely unknown. As well as the problems they mention, W. T. Tutte's snark conjecture concerns the existence of Petersen graphs as graph minors...

different spanning trees, each consisting of a single one of these edges. The Tutte polynomial of a graph can be defined as a sum, over the spanning trees of...