Vocabulary for Map Coloring

In the language of Mathematical Map Coloring, a map is not much different from the maps in an atlas. The areas which would be countries, states, counties, etc., on a political map are called regions. The lines that separate one region from another are called boundaries. Every region in a map is a closed curve because if it wasn't, the colors would leak out of the lines.

When a map is colored, the numer of colors used and their arrangement relative to one another is called a coloring of that map. A coloring that uses two colors is called a 2-coloring; if it uses 3 colors, it is called a 3-coloring, and so forth. Following the same pattern, a map that can be colored with two colors is called two-colorable. A short-cut way of expressing this is by using the variable n, and saying that a map that is n-colorable is a map that can be colored with n colors. You might demonstrate that a map is n-colorable by coloring it and showing people your n-coloring. (The number that you will use to replace the n, will, of course depend on the map you have colored and how you have colored it.)



See also:



What next?