• Thumbnail for Tutte theorem
    In the mathematical discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs...
    11 KB (1,397 words) - 10:15, 20 December 2024
  • 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...
    9 KB (960 words) - 08:07, 2 November 2024
  • 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...
    42 KB (4,642 words) - 06:57, 14 November 2024
  • Thumbnail for Tutte–Berge formula
    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...
    7 KB (969 words) - 00:36, 7 October 2023
  • provided by the Tutte theorem. A generalization of Hall's theorem to bipartite hypergraphs is provided by various Hall-type theorems for hypergraphs....
    21 KB (3,208 words) - 06:26, 15 June 2024
  • Thumbnail for Petersen's theorem
    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...
    13 KB (1,455 words) - 16:42, 28 September 2024
  • Planar graph (redirect from Theorem P)
    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...
    35 KB (4,541 words) - 12:22, 14 December 2024
  • 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...
    5 KB (540 words) - 05:09, 28 August 2024
  • 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...
    15 KB (2,010 words) - 01:24, 3 January 2024
  • In mathematics, the Tutte homotopy theorem, introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly...
    3 KB (477 words) - 20:02, 18 June 2022
  • factor-critical. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching. The Tutte theorem provides a characterization...
    7 KB (920 words) - 01:17, 30 October 2024
  • Tunnell's theorem (number theory) Tutte theorem (graph theory) Turán's theorem (graph theory) Turán–Kubilius theorem (number theory) Tverberg's theorem (discrete...
    73 KB (6,038 words) - 09:58, 20 November 2024
  • Thumbnail for Tatyana Ehrenfest
    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...
    4 KB (417 words) - 23:41, 13 September 2023
  • graphs. Hall's marriage theorem provides a characterization of bipartite graphs which have a perfect matching and the Tutte theorem provides a characterization...
    23 KB (2,938 words) - 19:04, 27 November 2024
  • Thumbnail for Component (graph theory)
    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...
    30 KB (3,441 words) - 12:55, 5 July 2024
  • force Tutte embedding Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595. "Lami's Theorem -...
    2 KB (422 words) - 03:04, 30 November 2024
  • 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...
    11 KB (1,261 words) - 07:56, 15 October 2024
  • 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...
    5 KB (638 words) - 17:14, 20 September 2023
  • 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...
    13 KB (2,031 words) - 07:14, 24 December 2024
  • Thumbnail for Hamiltonian path
    (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)...
    18 KB (2,030 words) - 19:28, 20 September 2024
  • Thumbnail for Tutte graph
    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...
    5 KB (697 words) - 20:43, 5 July 2021
  • two-dimensional Tutte embeddings into three dimensions using the Maxwell–Cremona correspondence, and methods using the circle packing theorem to generate...
    50 KB (5,973 words) - 15:13, 2 November 2024
  • Thumbnail for Graph coloring
    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...
    68 KB (8,081 words) - 05:15, 15 December 2024
  • Thumbnail for Kuratowski's theorem
    In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...
    9 KB (1,074 words) - 14:25, 7 November 2023
  • Thumbnail for Snark (graph theory)
    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...
    23 KB (2,707 words) - 02:29, 25 December 2024
  • Thumbnail for Tutte polynomial
    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...
    39 KB (5,377 words) - 18:30, 16 December 2024
  • In graph theory, the Nash-Williams theorem is a tree-packing theorem that describes how many edge-disjoint spanning trees (and more generally forests)...
    4 KB (464 words) - 11:17, 25 October 2024
  • contraction. Tutte refers to such a function as a W-function. The formula is sometimes referred to as the fundamental reduction theorem. In this article...
    4 KB (614 words) - 10:50, 25 October 2024
  • 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"...
    60 KB (8,755 words) - 14:58, 14 December 2024
  • Thumbnail for Spanning tree
    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...
    26 KB (3,265 words) - 23:16, 10 December 2023