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>but on real world maps, there are enclaves - little islands that belong to a country that they have not connection to. And if those shall have the same color as their parent country, then 4 colors is not enough...

Can you give an example of one that can't be colored with 4 colors?

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They all can be colored in 4 colors - if you don't care about giving the enclave the same color as the parent country.

If you insist giving those little islands the same color as the country they belong to, then things get difficult. That's not always doable in 4 colors.

see: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/4C...

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