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From: simon@psuvax.UUCP
Newsgroups: net.ai
Subject: Re: Fermat's Last Theorem
Message-ID: <447@psuvax.UUCP>
Date: Wed, 8-Feb-84 12:00:34 EST
Article-I.D.: psuvax.447
Posted: Wed Feb  8 12:00:34 1984
Date-Received: Sat, 11-Feb-84 08:00:57 EST
References: <16403@sri-arpa.UUCP> <189@pucc-i>
Organization: Pennsylvania State Univ.
Lines: 12

There is no graph, published in Scientific American or elsewhere, that is
planar and requires five colors. There were examples of graphs (I believe
there was one published in SA) for which simplistic 4-coloring strategies
failed. The proof is more than a computer listing: it consists of a strategy
for "discharging" (not original to  Haken & Appel), together with a recursive
proof that any  graph, after suitable discharging, is four-colorable iff a
certain set of irreducble graphs is. The computer was used both to help
with vrifying all cases of this proposition, and getting 4-colorings for the
1500 or so irreducible ones.
The computer program ran for a long time: it has never been formally certified
to be correct.
js