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In graph-theoretic terms, the theorem states that for a loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
This is an accepted version of this page This is the latest accepted revision, reviewed on 16 February 2025. For other color lists, see Lists of colors. This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "List of colors" alphabetical ...
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English: World map colored in green, yellow, blue and red to illustrate the four color theorem. This map considers just only land boundaries, although insular States have been colored too. This map considers just only land boundaries, although insular States have been colored too.
These are the lists of colors; List of colors: A–F; List of colors: G–M; List of colors: N–Z; List of colors (alphabetical) List of colors by shade; List of color palettes; List of Crayola crayon colors; List of RAL colours; List of X11 color names
Francis Guthrie (born 22 January 1831 in London; d. 19 October 1899 in Claremont, Cape Town) was a Cape Colony mathematician and botanist who first posed the Four Colour Problem in 1852. He studied mathematics under Augustus De Morgan, and botany under John Lindley at University College London. Guthrie obtained his B.A. in 1850, and LL.B. in ...
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With four colors, it can be colored in 24 + 4 × 12 = 72 ways: using all four colors, there are 4! = 24 valid colorings (every assignment of four colors to any 4-vertex graph is a proper coloring); and for every choice of three of the four colors, there are 12 valid 3-colorings. So, for the graph in the example, a table of the number of valid ...