Neliväriteoreema

Neliväriteoreema, also known as the Four Color Theorem, is a mathematical statement asserting that any map drawn on a plane can be colored using only four colors in such a way that no two adjacent regions share the same color. Adjacent regions are defined as those that share a common boundary, not merely a single point. The theorem applies to maps on a plane or a sphere, but not on surfaces with different topological properties, such as a torus.

The conjecture that four colors suffice was first formally stated in 1852 by Francis Guthrie, who was attempting to color a map of the counties of England. The problem remained unsolved for over a century, attracting the attention of many mathematicians. While various mathematicians claimed to have found proofs, these were often found to be flawed. The first widely accepted proof was provided in 1976 by Kenneth Appel and Wolfgang Haken, with assistance from John Koch. Their proof was highly controversial at the time because it relied heavily on computer assistance. They reduced the problem to a finite number of cases, which were then checked by a computer program.

Subsequent efforts have focused on simplifying the proof and reducing the reliance on extensive computer verification. More streamlined computer-assisted proofs have since been developed, making the theorem more accessible to the mathematical community. The Four Color Theorem is a classic example of a problem that was easy to state but incredibly difficult to prove, and its resolution had a significant impact on the development of computer science and proof techniques in mathematics.