four colour map theorem - meaning and definition. What is four colour map theorem
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What (who) is four colour map theorem - definition

STATEMENT IN MATHEMATICS
Four-Color Theorem; Four-color theorem; Four-colour theorem; Four colour problem; Four color problem; Four-color conjecture; Four Color Theory; Map-coloring problem; Four-Colour Map Problem; Four color map problem; Four-color problem; 4 color theorem; Four Color Theorem; 4CT; Four Colour Theorem; Four-colour problem; Four color map theorem; 4 colour map problem; Four-colour Theorem; Four-Colour Theorem; Four-color map theorem; 4-color conjecture; Four Color Conjecture; 4 color problem; 4-colors theorem; The Four-Color map Theorem; Map color problem; Proof of the 4 color theorem; History of the four color theorem; Four color conjecture; Four colour map problem; Four Color Problem; Map coloring problem; 4-color theorem; Seven colour theorem; 4-color problem; Four-Color Maps; Four-color map; Minimum number of map colors; Four colour theorem; 4 colour theorem; Four-colour map; Four-colour map problem; Four-color map problem; 4 color map problem; Four-Color Map Theorem
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  • 200px
  • Hamilton]], 23 Oct. 1852
  • Example of a four-colored map
  • A map with four regions, and the corresponding planar graph with four vertices.
  • A graph containing a Kempe chain consisting of alternating blue and red vertices
  • A four-colored map of the states of the United States (ignoring lakes and oceans)
  • This construction shows the torus divided into the maximum of seven regions, each one of which touches every other.
  • By joining the single arrows together and the double arrows together, one obtains a [[torus]] with seven mutually touching regions; therefore seven colors are necessary.

four colour map theorem      
<mathematics, application> (Or "four colour theorem") The theorem stating that if the plane is divided into connected regions which are to be coloured so that no two adjacent regions have the same colour (as when colouring countries on a map of the world), it is never necessary to use more than four colours. The proof, due to Appel and Haken, attained notoriety by using a computer to check tens of thousands of cases and is thus not humanly checkable, even in principle. Some thought that this brought the philosophical status of the proof into doubt. There are now rumours of a simpler proof, not requiring the use of a computer. See also chromatic number (1995-03-25)
four colour theorem         
four colour map theorem
Four color theorem         
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet.
https://en.wikipedia.org/wiki/Four_color_theorem

Wikipedia

Four color theorem

In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubters remain.

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). To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. In 2005, the theorem was also proved by Georges Gonthier with general-purpose theorem-proving software.

https://en.wikipedia.org/wiki/Four color theorem
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