Four color theorem

thumb|An illustration of the four color theorem in a political world map.In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

Description

Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.

Not of interest to mapmakers

Despite the motivation from coloring political maps of countries, the theorem is not of particular interest to mapmakers.

According to an article by the math historian Kenneth May:

Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of mapmaking do not mention the four-color property.

See also

• Discrete geometry
• Mathematics
• Apollonian network
• Graph coloring
• Grötzsch's theorem, triangle-free planar graphs are 3-colorable.
• Hadwiger–Nelson problem, how many colors are needed to color the plane so that no two points at unit distance apart have the same color?

External links

• Four color theorem @ Wikipedia