Every Planar Map Is Four Colorable

  title={Every Planar Map Is Four Colorable},
  author={Kenneth Appel and Wolfgang Haken},
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… Expand
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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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Untersuchungen zum Vierfarbenproblem