Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.08 10/3/83; site psuvax.UUCP Path: utzoo!watmath!clyde!akgua!sb1!sb6!bpa!burdvax!psuvax!simon 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