Every Planar Map Is Four Colorable

  title={Every Planar Map Is Four Colorable},
  author={Kenneth Appel and Wolfgang Haken},
  journal={Mathematical Solitaires \& Games},
  • K. Appel, W. Haken
  • Published 19 March 2019
  • Mathematics
  • Mathematical Solitaires & Games
As has become standard, the four color map problem will be considered in the dual sense as the problem of whether the vertices of every planar graph (without loops) can be colored with at most four colors in such a way that no pair of vertices which lie on a common edge have the same color. The restriction to triangulations with all vertices of degree at least five is a consequence of the work of A. B. Kempe. Over the past 100 years, a number of authors including A. B. Kempe, G. D. Birkhoff… 
Colouring planar graphs
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A simple necessary and sufficient condition is given for the vertices of a graph, planar or not, to be properly four-colorable. This criterion involves the notion of an "even" triangulation of S3 and
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T he four-color theorem [1, 2] is one of the most well-known results in graph theory. Originating from the question of coloring a world map, posed in the middle of the nineteenth century, it has
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A thesis submitted The famous Four Color Theorem states that any planar graph can be properly colored using at most four colors. However, if we want to properly color the square of a planar graph (or
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Questions raised by Dan Younger in 1987 helped us to provide an appropriate level of detail in the sections on immersion reducibility in the appendix to Part II
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Bibliographisches Institut
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Kempe chains and the four color problem, Utilitas Math
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then high school students and undergraduates) for aiding in checking the diagrams in the preprints for the papers
  • In addition,
  • 1977