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A coloring of plane regions, Link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems generally involve Topological considerations (i.e., they depend on the abstract study of the arrangement of objects), and theorems about colorings, such as the famous Four-Color Theorem, can be extremely difficult to prove.
See also Colorable, Edge-Coloring, Four-Color Theorem, k-Coloring, Polyhedron Coloring, Six-Color Theorem, Three-Colorable, Vertex Coloring
References
Eppstein, D. ``Coloring.''
http://www.ics.uci.edu/~eppstein/junkyard/color.html.
Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, 1986.