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Re: [HM] 7 Color theorem
Posted:
Nov 1, 2000 1:49 PM


Heawood's original paper, titled "MapColour Theorem," appeared in the Quarterly Journal of Pure and Applied Mathematics, vol. 24 (1890), pp. 332338. The pertinent excerpt is reprinted in the book "Graph Theory 17361936," by Biggs, Lloyd and Wilson (Oxford University Press, 1976), pp. 112115. There is an figure there of a torus map needing 7 colors. I assume it's an exact reproduction of what's in the original paper. Perhaps someone with access to the Quarterly Journal can confirm that.
My reason for assuming it's exact is that Biggs et al. also reprint Kempe's 1879 "proof" of the 4color theorem, which appeared in the American Journal of Mathematics, and the figures there are identical with those in a fascimile version of AJM available online through JSTOR ( http://www.jstor.org  but you need an institutional membership to do any searches). Again, perhaps someone with access to the original can confirm that JSTOR's version is exact. (I'm pretty sure it is. I think what you see at JSTOR are scanned versions of the actual journals.)
In his 1879 paper, Kempe describes (in words) a map on a torus that requires 6 colors. Presumably Heawood was the first person to find one that needs 7.
Barry Cipra cipra@microassist.com
> From: samuelskutler@webtv.net (Samuel S. Kutler) > Date: Tue, 31 Oct 2000 15:53:36 0500 (EST)
> > Where can I find a diagram of a map on a torus that requires seven > colors? > > Is there an original paper by Heawood with such an illustration?



