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

On Jun 14, 7:10 pm, bill <b92...@xxxxxxxxx> wrote:
On Jun 14, 4:10 pm, Gerry Myerson <g...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:



In article <f4sg45$30n...@xxxxxxxxxxxxxxxxxxxxxxx>,
rich...@xxxxxxxxxxxxxxx (Richard Tobin) wrote:

In article <1181860364.688539.71...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Andre <andre.robe...@xxxxxxxxx> wrote:

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

Even though there's a problem, it's still a good try. (Not all good
ideas pan out.)

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?

And maybe the easiest way to see that the reasoning is fallacious
is to draw yourself a map that needs 4 colors even though there
are no 4 different countries each bordering the other 3.

The easiest example I can think of is a map of the USA; look at Nevada
and the states surrounding it.

Just because the sqrt of 2 is rational is no reason to think that
the sqrt of 5 is also rational.

I think Bill meant to say "irrational" here --- if not, then HE is
irrational 8-) --- but the idea of "A map that requires K colors needs
to have K regions all adjacent to each other" is easily seen to be
false for K = 3 and 4, so it could easily be false for K = 5.

In any case, the burden is on the prover to establish something which
is not immediately, obviously true.

--- Christopher Heckman


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