====== Four Color Theorem ======
{{tag>#Resolved!}}

**''The 'Resolved' category archives questions which have been answered since they were added to the site.''**

''As of Apr. 2019, this entry is now moved to the 'Resolved' section. This theorem is widely regarded as having been solved. See : [[http://www.ams.org/notices/200811/tx081101382p.pdf|Formal Proof—The Four-Color Theorem]] //Notices of the AMS //Volume 55, Number 11.''\\ \\ '' For reference, the original text of the Wikenigma article is archived below :''

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The Four Color 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.// Source : [[https://en.wikipedia.org/wiki/Four_color_theorem|Wikipedia]]

Computational tests, checking millions of possible configurations, have never found an exception. (note that a formal proof with 5 colors was made in the late 19th century by Percy Heawood, see[[https://en.wikipedia.org/wiki/Percy_John_Heawood|Wikipedia]] ).

A 'machine generated proof' was described by Georges Gonthier of Microsoft Research Cambridge England, in 2007. //See:// [[https://link.springer.com/chapter/10.1007/978-3-540-87827-8_28|Asian Symposium on Computer Mathematics, ASCM 2007]] Asian Symposium on Computer Mathematics, ASCM 2007: Computer Mathematics pp 333-333