Answers 377- THE FOUR-COLOR MAP THEOREM
With two or more contiguous countries, two colors at least are obviously
necessary (Figure I). If three countries are contiguous each with each, three
colors are necessary (Figure 2). With four countries, three will be required if
the fourth (Y) is contiguous with each of two that are already contiguous
(Figure 3). (For, as in Figure 4, G may be contiguous with two countries not
contiguous with one another, when only two colors are needed.) And four
colors will be necessary if the fourth country is contiguous with each of three
already contiguous each with each (Figure 5).
With five contiguous countries, three will be required if one country is con-
tiguous with two already contiguous (Figure 6). And four will be necessary
if the fifth country is contiguous with each of three countries that are contig-
uous each with each (Figure 7). Yet five colors would be needed if a fifth