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Professor Thomas L. Saaty
Department of Mathematics
Universtity of Pittsburgh
Pittsburgh, PA  15213
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Dear Professor Saaty:

	I just bought your book with Paul Kainen on the four
color problem and am enjoying it.  You might be interested in
the following trivial map coloring algorithm that works well
on all real maps I could find---the U.S., the departments of
France, Europe and Asia, Africa, South America and also your
figure 2-32.

	Consider a country with three or fewer neighbors.
However, the rest of the map is colored, a color will be
available for it.  Therefore, all such countries may be
removed from the map for coloring later.  But the remaining
map may now have some countries with three or fewer neighbors.
They can be removed and the process continued until a reduced
map is obtained every country of which has four or more
neighbors.  In all the above cases the reduced map is empty.

	If we plan to use Kempe transformations, we
can extend the algorithm to delete countries with four or fewer
neighbors.  However, I haven't found a real map for which
this is required.  Naturally, the method doesn't color the
Heawood counterexample, your figure 2-15, because there every
country has five or more neighbors.

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Sincerely,
John McCarthy

\ps
P.S.  The United States can be colored with three colors if
we delete Kentucky and Nevada, the only states whose
numbers of neighbors is an odd number greater than three.
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