World maps are not mathematical maps. There is one additional country on the former, the country of mermaids. The color of the sea is the fifth color we need when we want to color the world map.
There were many people who traveled the country of mermaids. Sailors sailed to other countries and conquered them. Throw a glance at the map, what do you see? Is Hawaii a part of the USA, Columbia, Japan or India? The History can tell you that but Geography (i.e. the map) cannot.
Today one does not need to have sailors in order to invade another country; one only needs soldiers on airplanes or even less (soulless drones or computer viruses). Therefore my version of the Four color theorem is this:
Let n be the number of countries. The number of colors needed to color the world map is n+1.
Color the map accordingly and you do not need any additional assumptions (i.e. History) to answer the question “Which country does Hawaii belong to?” To answer your questions, that is what the political maps are for.