Page "Four color theorem" Paragraph 4

Three colors are adequate for simpler maps, but an additional fourth color is required for some maps, such as a map in which one region is surrounded by an odd number of other regions that touch each other in a cycle.

The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century ; however, proving that four colors suffice turned out to be significantly harder.

A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.