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In graph theory the road coloring theorem, known previously as the road coloring conjecture, deals with synchronized instructions.The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network (which might be a representation of city streets or a maze). [1]
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Their names are given by the color of the water. Sometimes a system of color symbolism was used as the following method green or light blue for east, black or dark for north, white for west, and red for south. This method is called cardinal directions. [1] There are other theories but these two methods of colors are also used.
Exact coloring of the complete graph K 6. Every n-vertex complete graph K n has an exact coloring with n colors, obtained by giving each vertex a distinct color. Every graph with an n-color exact coloring may be obtained as a detachment of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the ...
Direction determination refers to the ways in which a cardinal direction or compass point can be determined in navigation and wayfinding.The most direct method is using a compass (magnetic compass or gyrocompass), but indirect methods exist, based on the Sun path (unaided or by using a watch or sundial), the stars, and satellite navigation.
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The following discussion is a summary based on the introduction to Every Planar Map is Four Colorable (Appel & Haken 1989). Although flawed, Kempe's original purported proof of the four color theorem provided some of the basic tools later used to prove it. The explanation here is reworded in terms of the modern graph theory formulation above.