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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.
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.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
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).
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 ...
English: This is a map of France 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 function FindVertexColoring and GeoRegionValuePlot ...
Stake. Gradient maps are both at the center and at the basic level of map making on Wikipedia. A simple blank map and fill with color tool are needed. To continue to build a coherent Wikipedia display, this page suggests the most suitable SVG source files together with a blue-based color ramps from academic, screen friendly, print friendly, and color-blind friendly ColorBrewer2 by cartography ...
Image:Map of USA-bw.png – Black and white outlines for states, for the purposes of easy coloring of states. Image:BlankMap-USA-states.PNG – US states, grey and white style similar to Vardion's world maps. Image:Map of USA with county outlines.png – Grey and white map of USA with county outlines.