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apparently things like exclaves were intentionally omitted for simplicity’s sake.

That may not be just for simplicity’s sake. If you include “things like enclaves”, the graph may not be planar.

For example, Belgium, France, Germany and the Kingdom of the Netherlands all border each other (France and the Netherlands on Saint Martin (https://en.wikipedia.org/wiki/Saint_Martin_(island)), so if you take ”the Kingdom of the Netherlands” as a node, you can’t draw the graph on a plane.

An alternative is to see the countries of the Netherlands and St. Maarten as separate; https://en.wikipedia.org/wiki/Kingdom_of_the_Netherlands). That would remove this counterexample, but others may exist.

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