And well, it’s actually mathematically proven, but not for maps with disjointed regions that need to be colored the same, such as Alaska + mainland USA.
(In that particular case, it’s not too difficult to resolve, but you don’t get a guarantee for it.)
The map in the post actually merges such disjointed regions, though, so it absolutely should work there.
It’s the Four Color Theorem.
And well, it’s actually mathematically proven, but not for maps with disjointed regions that need to be colored the same, such as Alaska + mainland USA.
(In that particular case, it’s not too difficult to resolve, but you don’t get a guarantee for it.)
The map in the post actually merges such disjointed regions, though, so it absolutely should work there.