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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- P. Erdns, A. L. Rubin and H. Taylor: Choosability in graphs, Proc. West Coast Conference on Combinatorics, Graph Theory and Computing, Congres-sus Numerantium 26 (1979), 125–157.Google Scholar