Re: I have correct proof of 4-color theorem


cuishitai12000@xxxxxxxxxxxx wrote:
> Proginoskes 写道：
>
> > cuishitai@xxxxxxxxx wrote:
> > > The only correct, simple and elegant proof of
> > > the 4-color theorem [...]
> >
> > I can stop reading right here, because you're a crank. In fact, I could
> > have stopped at the first word ("the") because there are many proofs of
> > a result. (A few dozen of the Pythagorian Theorem, for instance.)
>
> But for 4CT there is only one computer proof, not any one by hand.

That is incorrect; there are at least _two_ computer proofs, one by
Appel and Haken (which is presumably the one you're referring to), and
another one by Robertson, Sanders, Seymour, and Thomas, which came out
in the mid 1990s. (I did some "grunt work" on this one.)

I also know of another alleged proof, which doesn't use computers, and
yet another one which uses "spiral chains" to 4-color a planar graph.

> > If you claim you have _a_ correct, elegant proof of the 4CT, feel free
> > to post it, though. Just as long as you're not saying that it's
> > impossible for five regions to share a common boundary edge. (The
> > 5-regions result was proved in 1840 by Augustus Moebius, before the
> > history of the 4CT, and is a RESULT of the 4CT, but it doesn't PROVE
> > it.)
>
> Do you nean every plane graph is 5-colorable?

No. Among amateurs, there is some confusion between the two statements
"any plane graph can be 4-colored", and "you cannot have 5 regions of
the plane, every pair of which are adjacent". I'm calling the second
statement "the 5-regions result", to avoid repetitively repeating
myself over and over again.

> In fact my proof is for any plane graph is 4-colorable.

That statement is false and is technically not what's referred to as
the 4 Color Theorem; in fact, I have a counter example to it: a graph
with one vertex, with a loop connecting that vertex to itself. That
graph is planar and not colorable _at all_.

I suspect you meant to say: "Every _loopless_ plane graph is
4-colorable", which _is_ the 4 Color Theorem.

> If not so, would you please say more detail as my English is poor, can
> not catch you your meaning. You may use some refering book.

It's just being careful and saying what you mean, and meaning what you
say.

--- Christopher Heckman

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