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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.
In optics, chromatic aberration (CA), also called chromatic distortion, color aberration, color fringing, or purple fringing, is a failure of a lens to focus all colors to the same point. [ 1 ] [ 2 ] It is caused by dispersion : the refractive index of the lens elements varies with the wavelength of light .
The problem asks if it is possible to color each of the positive integers either red or blue, so that no Pythagorean triple of integers a, b, c, satisfying + = are all the same color. For example, in the Pythagorean triple 3, 4, and 5 ( 3 2 + 4 2 = 5 2 {\displaystyle 3^{2}+4^{2}=5^{2}} ), if 3 and 4 are colored red, then 5 must be colored blue.
The aim of color calibration is to measure and/or adjust the color response of a device (input or output) to a known state. [1] In International Color Consortium (ICC) terms, this is the basis for an additional color characterization of the device and later profiling. [ 2 ]
Graph coloring has been studied as an algorithmic problem since the early 1970s: the chromatic number problem (see section § Vertex coloring below) is one of Karp's 21 NP-complete problems from 1972, and at approximately the same time various exponential-time algorithms were developed based on backtracking and on the deletion-contraction ...
Zwicky developed this approach to address seemingly non-reducible complexity: using the technique of cross-consistency assessment (CCA), [1] the system allows for reduction by identifying the possible solutions that actually exist, eliminating the illogical solution combinations in a grid box rather than reducing the number of variables involved.
One strategy for solving this version of the hat problem employs Hamming codes, which are commonly used to detect and correct errors in data transmission. The probability for winning will be much higher than 50%, depending on the number of players in the puzzle configuration: for example, a winning probability of 87.5% for 7 players.
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).