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The user selects the color corresponding to one of the numbers then uses it to fill in a delineated section of the canvas, in a manner similar to a coloring book. The kits were invented, developed and marketed in 1950 by Max S. Klein, an engineer and owner of the Palmer Paint Company in Detroit, Michigan, United States, and Dan Robbins, a ...
The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f(v) to each vertex v, a graph G is f-choosable (or f-list-colorable) if it has a list coloring no matter how one assigns a list of f(v) colors to ...
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
Above:A 3:1-coloring of the cycle on 5 vertices, and the corresponding 6:2-coloring. Below: A 5:2 coloring of the same graph. A b-fold coloring of a graph G is an assignment of sets of size b to vertices of a graph such that adjacent vertices receive disjoint sets. An a:b-coloring is a b-fold coloring out of a available colors.
In graph theory, circular coloring is a kind of coloring that may be viewed as a refinement of the usual graph coloring. The circular chromatic number of a graph G {\displaystyle G} , denoted χ c ( G ) {\displaystyle \chi _{c}(G)} can be given by any of the following definitions, all of which are equivalent (for finite graphs).
Some of these areas correspond to the older division, as is true regarding number theory (the modern name for higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry.
Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color; thus χ H (G) ≤ | V(G) |. There trivially exist graphs G with χ H (G) > χ(G) (where χ is the chromatic number); one example is any path of length > 2, which can be 2-colored but has no harmonious coloring with 2 colors. Some properties of χ H ...
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