Has the Four Color Theorem been proven?

The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map).

How was the 4 color map Problem solved?

four-colour map problem, problem in topology, originally posed in the early 1850s and not solved until 1976, that required finding the minimum number of different colours required to colour a map such that no two adjacent regions (i.e., with a common boundary segment) are of the same colour.

How long did it take to prove the 4 Colour map theorem?

[1]. A computer-assisted proof of the four color theorem was proposed by Kenneth Appel and Wolfgang Haken in 1976. Their proof reduced the infinitude of possible maps to 1,936 reducible configurations (later reduced to 1,476) which had to be checked one by one by computer and took over a thousand hours [1].

How does the Four Color Theorem work?

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color. This problem is sometimes also called Guthrie’s problem after F.

Who proved the 4 color theorem?

A computer-assisted proof of the four color theorem was proposed by Kenneth Appel and Wolfgang Haken in 1976. Their proof reduced the infinitude of possible maps to 1,936 reducible configurations (later reduced to 1,476) which had to be checked one by one by computer and took over a thousand hours [1].

How does the four color theorem work?

Do you need four colors to color a map?

You only need four colors to color all the regions of any map without the intersection or touching of the same color as itself. The beauty of this theorem lies in the fact it applies to all maps, regardless of their complexity or density of demarcations.

How is the four color theorem hard to prove?

The Four Color Theorem is one of many mathematical puzzles which sharethe characteristics of being easy to state, yet hard to prove. Very simplystated, the theorem has to do with coloring maps. Given a map of countries, can every map be colored(using dierent colors for adjacent countries)in such a way so that you only use four colors?

How did Appel and Haken prove the four color conjecture?

Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.

Can a planar graph be colored with 7 colors?

So no minimal criminal can exist and all graphs are 6-colorable. Any “minimal criminal” planar graph requiring 7 colors can be recolored with 6 colors using this method. Therefore, any planar graph can be colored using 6 colors (you will never need 7 or more).