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Topic: [HM] 7 Color theorem
Replies: 5   Last Post: Nov 1, 2000 6:54 PM

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Barry Cipra

Posts: 21
Registered: 12/3/04
Re: [HM] 7 Color theorem
Posted: Nov 1, 2000 1:49 PM
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Heawood's original paper, titled "Map-Colour Theorem," appeared in the
Quarterly Journal of Pure and Applied Mathematics, vol. 24 (1890), pp.
332-338. The pertinent excerpt is reprinted in the book "Graph Theory
1736-1936," by Biggs, Lloyd and Wilson (Oxford University Press, 1976),
pp. 112-115. 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 4-color 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
( - 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

> From: (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?

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