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Five-coloring plane graphs

  • Martin Aigner
  • Günter M. Ziegler

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Fachbereich Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

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