ECS 110
Data Structures and Programming
Assignment #5
Due Date
Thursday, March 15, 2007
The Problem
The most famous mathematical problem of this century is certainly the four-color problem.
The problem, simply stated, is the following:
Suppose you draw a map on a piece of paper -- any map. What is the minimum
number of colors you can use to color this map, with the restriction that no two
neighboring "countries" get the same color?
It is quite easy to see that you cannot do it in general with three colors, and you can
always do it with five. So the problem is: Are there maps that could not be colored with
four colors? Or, alternatively, could you always color a map with four colors?
Kenneth Appel and Wolfgang Haken, who exhibited methods that cleverly segmented the
map into a large number of submaps, solved this problem in 1976. They showed that if
each submap could be colored with four colors, then the entire map could also be colored
with four colors. They proved that all the submaps could be colored by “coloring” the
individual submaps with a computer system.
Your assignment is do the same thing that they did, except with the following map. Show
it can be colored with only four colors. (Hint: Can you see the graph in this problem?)
