Re: Four color theorem: why this is not a proof and pointer to simple explanations

In article <1181860364.688539.71120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Andre <andre.roberge@xxxxxxxxx> wrote:

Here's the "proof"; I suspect that the problem is right with the first
step.

1. If there is a map where 5 colors are needed, it must be because 5
different countries are touching each other.

You're right. You need to prove this. How can you be sure there
aren't other configurations that somehow force 5 colours? It's true
of course, since the four colour theorem is true: the are no maps
where 5 colours are needed, so all of them have 5 mutually touching
regions. But no proof of it is known other than the proof of the
four colour theorem.

I believe many mathematicians have made the same erroneous first step
in trying to prove the theorem.

-- Richard
--
"Consideration shall be given to the need for as many as 32 characters
in some alphabets" - X3.4, 1963.
.

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