Computability of five-color maps

Aside from the mathematical question as to whether any planar map can be colored with four or five colors so that no adjacent regions are assigned the same color, there is a computational problem of finding a coloration for a given map. This report presents an algorithm for the five-color problem which has an asymptotic computing time which is proportional to the square of the number of regions, at worst. The algorithm can be modified to produce six-color maps in linear time. The algorithm has been implemented for practical use in an image processing system and can be used in practical cases to produce four-color maps.