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Five-coloring plane graphs

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Proofs from THE BOOK

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Abstract

Plane graphs and their colorings have been the subject of intensive research since the beginnings of graph theory because of their connection to the four-color problem. As stated originally the four-color problem asked whether it is always possible to color the regions of a plane map with four colors such that regions which share a common boundary (and not just a point) receive different colors. The figure on the right shows that coloring the regions of a map is really the same task as coloring the points of a plane graph. As in Chapter 10 (page 57) place a point in the interior of each region (including the outer region) and connect two such points belonging to neighboring regions by a line through the common boundary.

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References

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Authors and Affiliations

  1. Institut für Mathematik II (WE2), Freie Universität Berlin, Arnimallee 3, D-14195, Berlin, Germany

    Martin Aigner

  2. Fachbereich Mathematik, MA 7-1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Günter M. Ziegler

Authors
  1. Martin Aigner
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  2. Günter M. Ziegler
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© 1998 Springer-Verlag Berlin Heidelberg

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Aigner, M., Ziegler, G.M. (1998). Five-coloring plane graphs. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22343-7_25

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  • DOI: https://doi.org/10.1007/978-3-662-22343-7_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-22345-1

  • Online ISBN: 978-3-662-22343-7

  • eBook Packages: Springer Book Archive

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