Four color theorem - why is this considered wrong?

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Rainy Monday
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Joined: Sun Sep 25, 2011 3:55 pm

Four color theorem - why is this considered wrong?

Post by Rainy Monday »

I'd like to think I found a proof for the four color theorem, but I also know that it took far smarter people than me a computer simulation to prove. Still, I don't see why this logic should be flawed. If you'd explain to me plainly, I'd love it:

1- The best case scenario for two differently-colored regions allows the other regions to be inside or outside, like this:
Image

2a- If the third region is inside, the best case scenario allowing the most amount of possibilities is something like this:
Image

3a- Then the fourth differently-colored region must be in one of the gaps. Let it be the top right gap:
Image

4a- Then all the gaps will have 3 colors around them just like in the previous stage, and no progress will be made.

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2b- If the third region is outside, it's something like this:
Image

3b- To avoid 4a, let the fourth also be outside:
Image

4b- While trying to avoid 4a, we end up with a similar situation to 3b with only 3 exterior regions to surround.
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