DescriptionVisual proof USA states map needs 4 colors.svg
English: Proof without words that a map of US states needs at least 4 colors so that states sharing land borders (disregarding the quadripoint) have different colors by CMG Lee. For example, landlocked Missouri (MO) has 8 neighbors (even). It must be differently colored from all of them, but the neighbors can alternate colors, thus this part of the map needs only 3 colors. However, landlocked Nevada (NV) has 5 neighbors (odd). One of the neighbors must be differently colored from it and all the others, thus 4 colors are needed. The map is from http://commons.wikimedia.org/wiki/File:Blank_US_Map_(states_only).svg .
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Proof without words that a map of US states needs at least 4 colors so that states sharing land borders (disregarding the quadripoint) have different colors
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Short title
Visual proof USA states map needs 4 colors
Image title
Proof without words that a map of US states needs at least 4 colors so that states sharing land borders (disregarding the quadripoint) have different colors by CMG Lee. For example, landlocked Missouri (MO) has 8 neighbors (even). It must be differently colored from all of them, but the neighbors can alternate colors, thus this part of the map needs only 3 colors. However, landlocked Nevada (NV) has 5 neighbors (odd). One of the neighbors must be differently colored from it and all the others, thus 4 colors are needed. The map is from http://commons.wikimedia.org/wiki/File:Blank_US_Map_(states_only).svg .