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The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider.
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 ...
A coloring using at most k colors is called a (proper) k-coloring. The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G). [4] Sometimes γ(G) is used, since χ(G) is also used to denote the Euler characteristic of a graph. [5]
The set of colors could also depend on the state of the game; for instance it could be required that the color used be different from the color used on the previous move. The map-based constraints on a move are usually based on the region to be colored and its neighbors, whereas in the map-coloring problem , regions are considered to be ...
For instance, complete edge coloring is the edge-coloring variant of complete coloring, a proper edge coloring in which each pair of colors must be represented by at least one pair of adjacent edges and in which the goal is to maximize the total number of colors. [21] Strong edge coloring is the edge-coloring variant of strong coloring, an edge ...
Col is a pencil and paper game, specifically a map-coloring game, involving the shading of areas in a line drawing according to the rules of graph coloring.With each move, the graph must remain proper (no two areas of the same colour may touch), and a player who cannot make a legal move loses.
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