explain four coluour theorem
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the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the 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.[1] 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.[2] Since then the proof has gained wide acceptance, although some doubters remain.[3]
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The 4-color theorem is fairly famous in mathematics for a couple of reasons. First, it is easy to understand: any reasonable map on a plane or a sphere (in other words, any map of our world) can be colored in with four distinct colors, so that no two neighboring countries share a color.
A graph is said to be n-colorable if it's possible to assign one of n colors to each vertex in such a way that no two connected vertices have the same color. Obviously the above graph is not 3-colorable, but it is 4-colorable. The Four Color Theorem asserts that every planar graph - and therefore every "map" on the plane or sphere - no matter how large or complex, is 4-colorable. Despite the seeming simplicity of this proposition, it was only proven in 1976, and then only with the aid of computers.
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