Four color theorem
In real life, many countries have exclaves or colonies. Since they belong to the country, they need to be colored with the same color as the parent country. This means that usually, more than four colors are needed to color such a map. When mathematicians talk about the graph associated with the problem, they say that is not planar. Even though it is easy to check if a graph is planar, finding the fewest number of colors needed to color it is very difficult. It is NP-complete, which is one of the most difficult problems that exist. The fewest number of colors needed to color a graph is known as its chromatic number. Many of the problems that happen when trying to solve the four color theorem are related to discrete mathematics. For this reason, methods from algebraic topology are often used.