[dmurray]

Four colours also isn't enough for some real-world country maps. Countries with enclaves (like Alaska, Kaliningrad or Sint-Maarten, though only the last actually makes 4- colouring impossible) change the topology: you can think of what shape the earth would have if there was also a tunnel connecting Alaska and New York.

[Blammar]

Torus, of course, but how does that relate to enclaves, which are planar ?

[dmurray]

You might want to colour the exclave the same colour as the rest of its country, even though no connection can exist between them on the plane.

[etbebl]

It seems like you're using "enclave" and "exclave" interchangeably, which is causing confusion. What you're referring to is an exclave; an enclave is when one region is completely surrounded by another, like Lesotho or Vatican City.

[dmurray]

You're right, my first post should say exclaves and the three examples I gave are all exclaves.