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From: davy@ecn-ee.UUCP
Newsgroups: net.ai
Subject: Re: Re: Four color... - (nf)
Message-ID: <1622@pur-ee.UUCP>
Date: Wed, 22-Feb-84 17:19:00 EST
Article-I.D.: pur-ee.1622
Posted: Wed Feb 22 17:19:00 1984
Date-Received: Fri, 24-Feb-84 01:40:18 EST
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Organization: Electrical Engineering Department , Purdue University
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#R:mit-eddi:-129000:ecn-ee:15300005:000:1121
ecn-ee!davy    Feb 22 08:38:00 1984


Thanks to all who responded about my question of "what is the four
color problem".  For those of you who also don't know, a brief
explanation (from sdcrdcf!darrelj) is:

	A long time conjecture in mathematics was that any planar 
	map of regions (e.g. the United States minus anomalies like 
	a two-piece Michigan) could be colored in such a way that 
	every pair of regions which share a border are different 
	color using no more than 4 distinct colors (also, sharing a 
	single finite number of points only do NOT share a border). 

	It was believed true for the last 100 years (and many 
	erroneous proofs were offerred), until a few years ago, 
	mathemeticians at U. of Illinois generated a proof, the 
	short part of which said "all graphs without properties xxx 
	can be four-colored, the long part of which was a computer 
	generation of all the thousands of graphs with the messy 
	properties combined with an enumeration of how to color each 
	one. 

	There are related kinds of problems for other topological 
	surfaces such as the surface of a sphere and the surface of 
	a torus (doughnut). 

--Dave Curry