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In graph-theoretic terms, the theorem states that for 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.
George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem.If (,) denotes the number of proper colorings of G with k colors then one could establish the four color theorem by showing (,) > for all planar graphs G.
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 ...
SVG Version of X11 color names SVG1.1 named colors with sRGB hex/dec and HSL codes, at UHD (4K) resolution. Extended colors are the result of merging specifications from HTML 4.01, CSS 2.0, SVG 1.0 and CSS3 User Interfaces (CSS3 UI). [6] Several colors are defined by web browsers. A particular browser may not recognize all of these colors, but ...
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 ...
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 ...
A graph that requires four colors in any coloring, and four connected subgraphs that, when contracted, form a complete graph, illustrating the case k = 4 of Hadwiger's conjecture In graph theory , the Hadwiger conjecture states that if G {\displaystyle G} is loopless and has no K t {\displaystyle K_{t}} minor then its chromatic number satisfies ...
The CMYK color model is based on the CMY color model, which omits the black ink. Four-color printing uses black ink in addition to subtractive primaries for several reasons: [2] In traditional preparation of color separations, a red keyline on the black line art marked the outline of solid or tint color areas. In some cases a black keyline was ...