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  2. Four color theorem - Wikipedia

    en.wikipedia.org/wiki/Four_color_theorem

    Example of a four-colored map A four-colored map of the states of the United States (ignoring lakes and oceans). In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color.

  3. Heawood conjecture - Wikipedia

    en.wikipedia.org/wiki/Heawood_conjecture

    An entirely different approach was needed for the much older problem of finding the number of colors needed for the plane or sphere, solved in 1976 as the four color theorem by Haken and Appel. On the sphere the lower bound is easy, whereas for higher genera the upper bound is easy and was proved in Heawood's original short paper that contained ...

  4. List of incomplete proofs - Wikipedia

    en.wikipedia.org/wiki/List_of_incomplete_proofs

    Kempe's proof did, however, suffice to show the weaker five color theorem. The four-color theorem was eventually proved by Kenneth Appel and Wolfgang Haken in 1976. [2] Schröder–Bernstein theorem. In 1896 Schröder published a proof sketch [3] which, however, was shown to be faulty by Alwin Reinhold Korselt in 1911 [4] (confirmed by ...

  5. Discharging method (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Discharging_method...

    In 1904, Wernicke introduced the discharging method to prove the following theorem, which was part of an attempt to prove the four color theorem. Theorem: If a planar graph has minimum degree 5, then it either has an edge with endpoints both of degree 5 or one with endpoints of degrees 5 and 6.

  6. Conjecture - Wikipedia

    en.wikipedia.org/wiki/Conjecture

    The four color theorem was ultimately proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer. Appel and Haken's approach started by showing that there is a particular set of 1,936 maps, each of which cannot be part of a smallest-sized counterexample to the four color theorem (i.e., if ...

  7. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Foster's theorem ; Four color theorem (graph theory) Four functions theorem (combinatorics) Four-vertex theorem (differential geometry) Fourier inversion theorem (harmonic analysis) Fourier theorem (harmonic analysis) Franel–Landau theorem (number theory) Fraňková–Helly selection theorem (mathematical analysis) Fredholm's theorem (linear ...

  8. Tait's conjecture - Wikipedia

    en.wikipedia.org/wiki/Tait's_conjecture

    The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeless cubic planar graphs. In a Hamiltonian cubic planar graph, such an edge coloring is easy to find: use two colors alternately on the cycle ...

  9. List of graph theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_graph_theory_topics

    Four color theorem; Fractional coloring; Goldberg–Seymour conjecture; Graph coloring game; Graph two-coloring; Harmonious coloring; Incidence coloring; List coloring; List edge-coloring; Perfect graph; Ramsey's theorem; Sperner's lemma; Strong coloring; Subcoloring; Tait's conjecture; Total coloring; Uniquely colorable graph