Comment on What are the most mindblowing fact in mathematics?

• SgtAStrawberry@lemmy.world ⁨2⁩ ⁨years⁩ ago

  Looks to be that way one of the examples given on the wiki page. It is still however an interesting theory, if four countries touching at a corner, are the diagonal countries neighbouring each other or not. It honestly feels like a question that will start a war somewhere at sometime, probably already has.

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  • Vegasimov@reddthat.com ⁨2⁩ ⁨years⁩ ago

    In graph theory there are vertices and edges, two shapes are adjacent if and only if they share an edge, vertices are not relevant to adjacency. As long as all countries subscribe to graph theory we should be safe

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    • SgtAStrawberry@lemmy.world ⁨2⁩ ⁨years⁩ ago

      The only problem with that it that it requires all countries to agree to something, and that seems to become harder and harder nowadays.

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• Blyfh@lemmy.world ⁨2⁩ ⁨years⁩ ago

  But each small country has three neighbors! Two small ones, and always the big donut country. I attached a picture to my previous comment to make it more clear.

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  • Pronell@lemmy.world ⁨2⁩ ⁨years⁩ ago

    In your example the blue country could be yellow and that leaves the other yellow to be blue. Now no identical colors touch.

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    • wazoobonkerbrain@lemmy.world ⁨2⁩ ⁨years⁩ ago

      You still have two red countries touching each other, what are you talking about?

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      • Pronell@lemmy.world ⁨2⁩ ⁨years⁩ ago

        Oops I meant the red one goes blue.

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  • Afrazzle@sh.itjust.works ⁨2⁩ ⁨years⁩ ago

    Whoops I should’ve been clearer I meant two neighbours within the donut. So the inside ones could be 2 or 3 colours and then the donut is one of the other 2 or the 1 remaining colour.

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    • Blyfh@lemmy.world ⁨2⁩ ⁨years⁩ ago

      You’re right. Bad example from my side. But imagine the four small countries being four parts of another donut that encompass a smaller country. Then it would be impossible.

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      • Afrazzle@sh.itjust.works ⁨2⁩ ⁨years⁩ ago

        That map is actually still quite similar to the earlier example where all 4 donut hole countries are the same. Once again on the right is the adjacency graph for the countries where I’ve also used a dashed line to show the only difference in adjacency. Image

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      • neumast@lemmy.world ⁨2⁩ ⁨years⁩ ago

        Make purple yellow and one of the reds purple.

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• ikilledlaurapalmer@lemmy.world ⁨2⁩ ⁨years⁩ ago

  Image Ok now do this one. What color is the donut country?

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  • BewilderedBeast@mander.xyz ⁨2⁩ ⁨years⁩ ago

    Image

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  • Afrazzle@sh.itjust.works ⁨2⁩ ⁨years⁩ ago

    Someone beat me to it, so I thought I’d also include the adjacency graph for the countries, it can be easier to see the solution to colouring them. Image

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