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The original version consisted of one copy of each of the 24 different squares that can be made by coloring the edges of a square with one of three colors. (Here "different" means up to rotations.) The goal is to arrange the squares into a 4 by 6 grid so that when two squares share an edge, the common edge is the same color in both squares.
The mutilated chessboard problem itself was proposed by philosopher Max Black in his book Critical Thinking (1946), with a hint at the coloring-based solution to its impossibility. [ 3 ] [ 4 ] It was popularized in the 1950s through later discussions by Solomon W. Golomb (1954), [ 5 ] George Gamow and Marvin Stern (1958), [ 6 ] Claude Berge ...
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color.
Coloring the edges of the Petersen graph with three colors. [5] Seven Bridges of Königsberg – Walk through a city while crossing each of seven bridges exactly once. [6] Squaring the circle, the impossible problem of constructing a square with the same area as a given circle, using only a compass and straightedge. [7]
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A coloring is an assignment of a color to each vertex of V. A coloring is conflict-free if at least one vertex in each edge has a unique color. If H is a graph, then this condition becomes the standard condition for a legal coloring of a graph: the two vertices adjacent to every edge should have different colors.
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. One player tries to ...