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A color triangle is an arrangement of colors within a triangle, based on the additive or subtractive combination of three primary colors at its corners. An additive color space defined by three primary colors has a chromaticity gamut that is a color triangle, when the amounts of the primaries are constrained to be nonnegative.
The equitable chromatic number of a graph G is the smallest number k such that G has an equitable coloring with k colors. But G might not have equitable colorings for some larger numbers of colors; the equitable chromatic threshold of G is the smallest k such that G has equitable colorings for any number of colors greater than or equal to k. [2]
This subdivision of a triangle is a special case of a theorem of Richard Courant and Herbert Robbins that any plane area can be subdivided into four equal parts by two perpendicular lines, a result that is related to the ham sandwich theorem. [4] Although the triangle quadrisection has a solution involving the roots of low-degree polynomials ...
The problem is that the three primaries can only produce colors which lie withinin their gamut - the triangle in color space formed by the primaries, which never touches the monochromatic locus nor the purple line except at the three primaries. In other words, there is no monochromatic source that can be matched by a combination of the three ...
This is referred to as "drawing without replacement", by opposition to "drawing with replacement". multivariate hypergeometric distribution: the balls are not returned to the urn once extracted, but with balls of more than two colors. [3] geometric distribution: number of draws before the first successful (correctly colored) draw. [3]
As in Pascal's triangle and other similarly constructed triangles, [2] sums of components along diagonal paths in Bernoulli's triangle result in the Fibonacci numbers. [3] As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ≥ 2. [4]
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
Other Ramsey games are possible. For instance, the players can be allowed to color more than one line during their turns. Another Ramsey game similar to Sim and related to the Ramsey number R(4, 4) = 18 is played on 18 vertices and the 153 edges between them. The two players must avoid to color all six edges connecting four vertices.
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