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From: mcmillan@eosp1.UUCP (John McMillan)
Newsgroups: net.ai
Subject: Re: Four color...
Message-ID: <596@eosp1.UUCP>
Date: Fri, 17-Feb-84 15:33:24 EST
Article-I.D.: eosp1.596
Posted: Fri Feb 17 15:33:24 1984
Date-Received: Tue, 21-Feb-84 04:39:27 EST
References: <5540@uiucdcs.UUCP> <1290@mit-eddie.UUCP>
Organization: Exxon Office Systems, Princeton, NJ
Lines: 17

It was proved long ago that 7 colors suffices for a Torus.  I believe that
a sphere cannot require more colors than a plane.  The proofof this (?)
is as follows:

	You can convert a sphere into a plane by piercing a hole in it
	the size of a point, and then stretching it out flat.

	In a colored map, no countries meet at a point; they must share
	a border that has some length.

	Therfore piercing a hole in a spherical map does not change any
	of its boundary conditions, while converting it into a plane.
					- Toby Robison
					allegra!eosp1!robison
					decvax!ittvax!eosp1!robison
					princeton!eosp1!robison
					(NOTE! NOT McMillan; Robison.)