Re:Decades-Old Graph Problem Yields to Amateur Mathematician
by hermitdev on Tuesday April 17, 2018 @06:06PM
(#16862731)
Like I said, describing it is hard, but showing it is not See this: https://imgur.com/iU7oc8d There's no way to color that with 4 colors without a color hitting itself. Yes, it's contrived, but so are borders. Also, the 4-color theorem didn't limit itself to established borders, it claims to be for an arbitrary map. This image, is well, arbitrary and drawn up in paint in a few minutes, but it shows the point.
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Re:Decades-Old Graph Problem Yields to Amateur Mathematician
by Sniffnoy on Tuesday April 17, 2018 @06:12PM
(#16862770)
You're mistaken about that not being 4-colorable. Color the "rings", from outside to inside: red, blue, green, blue, yellow.
Again, as mentioned in my earlier comment, I would suggest thinking of things / describing things in terms of plane graphs rather than "maps". It'll make everything easier.
I might also suggest learning some of the relevant graph theory? It sounds like you're trying and failing to embed a K_5, or perhaps an arbitrary K_n, into the plane. That can't be done, and the proof that this is impossible is much easier than the full 4-color theorem. (There are also the 5-color and 6-color theorems, which again have much easier proofs than the 4-color theorem, and which are another reason you can't embed an arbitrary K_n in the plane.)