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In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.
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It indicates how to give color to geographic areas (common geopolitical delimitations: nations, regions, etc.). With the following steps: Choose the colors to paint the areas. Choose for one of two possibilities: Paint the areas of a blank map. Indicate that areas are still painted (only for maps of the world).
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English: World map colored in green, yellow, blue and red to illustrate the four color theorem. This map considers just only land boundaries, although insular States have been colored too. This map considers just only land boundaries, although insular States have been colored too.
In cartographic design, map coloring is the act of choosing colors as a form of map symbol to be used on a map. Color is a very useful attribute to depict different features on a map. [ 1 ] Typical uses of color include displaying different political divisions, different elevations, or different kinds of roads.
Blank area for creating Locator maps. Based on simplified Location maps. A province in the country (when the blank map is actually filled). /Area maps (en) Maps that highlight one subject area, primarily for species distributions. Locator maps: a country (red) in its region and in the world (corner map). Multi-area: ranges of animals species ...
English: This is a map of the contiguous United States with the District of Columbia where no two neighboring first-level administrative divisions have the same color, following the guidelines of the four-color theorem, which states that any loopless planar graph can be colored with four or fewer colors. This was created with Mathematica 13.2's ...