From: Karl Brace <brace@cadtls.enet.dec.com>
Newsgroups: rec.org.mensa,sci.logic,sci.math,sci.misc,alt.folklore.urban,alt.folklore.science,alt.folklore.computers,sci.philosophy.meta,sci.misc,comp.misc
Subject: Re: 4 Color Theorem
Date: Fri, 05 Dec 1997 07:56:09 -0500

I previously posted this reference to interesting 
information on the four color theorem, but not to so 
many newsgroups. It includes historical information 
about previous attempts to prove the theorem, and an 
easy to follow description of the most recent proof.

http://www.math.gatech.edu/~thomas/FC/fourcolor.html

I found it by searching at http://www.altavista.digital.com, 
advanced search, for title:"that four color theorem"
or title:"that four colour theorem"

Somebody at
http://allserv.rug.ac.be/~pruyss/cgi-bin/4CT.cgi
thinks he has a simpler proof and is asking people to 
review his manuscript.

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_four_colour_theorem.html
also has a very complete historical description of past 
work in this area.

http://www.math.columbia.edu/~cormac/p4.html also has a 
VERY simple proof that is VERY easy to understand, but
contains a flaw (and the author Cormac O' Sullivan 
challenges you to find the flaw).

Karl Brace
==============================================================================
From: cet1@cus.cam.ac.uk (Chris Thompson)
Newsgroups: rec.org.mensa,sci.logic,sci.math,sci.misc,alt.folklore.urban,alt.folklore.science,alt.folklore.computers,sci.philosophy.meta,sci.misc,comp.misc
Subject: Re: 4 Column Theorem
Date: 4 Dec 1997 12:52:22 GMT

[The newsgroup list is ridiculously long: followups set to sci.math] 

In article <34849187.B5577AB7@netcom.com>, Bob McQueer  <mcq@netcom.com> wrote:
[...]
>                                                            The general
>sufficiency result for spheres with a positive number of handles is
>called the "Heawood Coloring Theorem", demonstrated by Heawood in the
>late 19th century.  He also found the error in an accepted early proof of
>the 4 color theorem, and until recently the best anybody could prove for
>the 0 handles case (the sphere, which is equivalent to the plane) was
>that 5 colors was sufficient.  And the "necessary" end of the Heawood
>result wasn't proved until the 1950's, but still long before the proof of
>the FCT.

Actually the proof was not completed until the winter of 1967-1968. The 
chronology in Ringel's book gives the last special case (embedding of K_30
in the surface of appropriate genus) as "solved by Mayer at the the end of 
February and independently by Youngs in March 1968". The details of the 
various cases were published in a series of papers by Ringel & Youngs
in the Journal of Combinatorial Theory during 1969.

Whether you still want to call that "long before the proof of the 4CT"
no doubt depends on one's perspective.

Maybe you were thinking of the *non*-orientable case, which was finished
off by Ringel in 1954 (although the proofs were subsequently much simplified).

Chris Thompson
Email: cet1@cam.ac.uk