English: A map of the United States showing four colors, including the constraint that the surrounding land and water is also coloured. According to the Four color theorem, only four colors are needed to complete a map containing any type of shapes provided that two touching shapes share a border of at least two points (a line).

However, because both Michigan and Virginia have disjoint areas that are coloured the same, it is only by chance that this map can be four-coloured. It is possible for such maps, with the constraints that certain disjoint regions be coloured the same, need arbitrarily large numbers of colours.

This graphic uses a colour palette accessible to colour blind people.