Map coloring is the act of assigning different colors to different features on a map. There are two very different uses of this term. The first is in cartography, choosing colors as a form of Map symbol to be used on a map. The second is in mathematics, where the problem is to determine the minimum number of colors needed to color a map so that no two adjacent features have the same color.
Cartography
Color is a very useful attribute to depict different features on a map. Typical uses of color include displaying different political divisions, different elevations, or different kinds of roads. A choropleth map is a thematic map in which areas are colored differently to show the measurement of a statistical variable being displayed on the map. The choropleth map provides an easy way to visualize how a measurement varies across a geographic area or it shows the level of variability within a region. In addition to choropleth maps, a cartographer should strive to depict colors effectively on any kind of map. Displaying the data in different hues can greatly affect the understanding or feel of the map. In many cultures, certain colors have connotations. These connotations lie under a field of study called Color Symbolism. For example, coloring a certain nation a color that has a negative connotation in their culture could be counterproductive. Likewise, using assumed skin colors to show racial or ethnic patterns will likely cause offense. It is not possible to always predict the color connotations of every map reader or to avoid negative connotations, but it is helpful to be aware of common color connotations in order to make a map as appealing and understandable as possible. Cartographers may also chose to pick hues that are associated with what they are mapping. For example, when mapping precipitation, they may choose to use shades of blue or for a map of wildfires they may use yellows, reds, and oranges. Carefully choosing colors ensures that the map is intuitive and easy to read. This process is referred to as Feature Association. Also, the cartographer must take into account that many people have impaired color vision, and use colors that are easily distinguishable by these readers. A general rule is that most people can only differentiate between 5-8 different shades of one color, thus if the amount of data to be mapped requires more than 8, it is best to use multiple colors. Most GIS programs provide users with carefully curated color schemes to choose from, thus making the process of selecting colors easier. Colors can also be used to produce three-dimensional effects from two-dimensional maps, either by explicit color-coding of the two images intended for different eyes, or by using the characteristics of the human visual system to make the map look three-dimensional.
Mathematics
In mathematics there is a very strong link between map coloring and graph coloring, since every map showing different areas has a corresponding graph. By far the most famous result in this area is the four color theorem, which states that any planar map can be colored with at most four colors.
