Four Color Theorem

CORE DEFINITION

The four color theorem (also known as the four color map theorem) is a mathematical theorem: if some contiguous finite regions are drawn on a plane, they can be colored with four colors such that any two adjacent regions have different colors; another popular statement is that every map without exclaves can be colored with no more than four colors, and no two adjacent regions will have the same color. Two regions are called adjacent if they share a common boundary segment, not merely a common point. For example, in the circle at the lower left of the right figure, the red and green parts are adjacent regions, while the yellow and red parts are not adjacent. The question 'Is four colors always enough to color any map?' was first raised by South African mathematician Francis Guthrie in 1852, known as the 'four color problem' or 'four color conjecture'. It was found easy to prove the weaker 'five color theorem' (i.e., 'five colors are enough to color any map'), but the four color problem turned out to be unexpectedly difficult.