Four color theorem
In the real world, this is not true: Alaska as part of the United States, Nakhchivan as part of Azerbaijan, and Kaliningrad as part of Russia are not contiguous. Because the territory of a particular country must be the same color, four colors may not be enough. For instance, consider a simplified map, such as the one shown on the left: In this map, the two regions labeled A belong to the same country, and must be the same color. This map then requires five colors, since the two A regions together are contiguous with four other regions, each of which is contiguous with all the others. If A had only three regions, six or more colors might be needed. In this way, it is possible to make maps that need an arbitrarily high number of colors. A similar construction also applies if a single color is used for all bodies of water, as is usual on real maps.