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Example of necklace splitting with k = 2 (i.e. two partners), and t = 2 (i.e. two types of beads, here 8 red and 6 green). A 2-split is shown: one partner receives the largest section, and the other receives the remaining two pieces. Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory.
In color theory, color harmony refers to the property that certain aesthetically pleasing color combinations have. These combinations create pleasing contrasts and consonances that are said to be harmonious. These combinations can be of complementary colors, split-complementary colors, color triads, or analogous colors.
A complementary color scheme comprises two colors that combine to form gray, i.e. they are on opposite sides of the color wheel. Fully saturated complementary colors maximize color contrast. A split-complementary (also called compound harmony) color scheme comprises three colors, namely a base color and two colors that are 150 degrees and 210 ...
The "E" denotes that, on top of having k colors, each edge must contain exactly k vertices. The optimization version of this problem is called max set splitting and requires finding the partition which maximizes the number of split elements of F. It is an APX-complete [2] problem and hence in NPO.
Complementary colors are pairs of colors which, when combined or mixed, cancel each other out (lose chroma) by producing a grayscale color like white or black. [1] [better source needed] When placed next to each other, they create the strongest contrast for those two colors. Complementary colors may also be called "opposite colors".
In Chevreul's 1839 book The principles of harmony and contrast of colours, [12] he introduced the law of color contrast, stating that colors that appear together (spatially or temporally) will be altered as if mixed with the complementary color of the other color, functionally boosting the color contrast between them. For example, a piece of ...
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).
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.
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