Teorema das cinco cores: uma aplicação da teoria dos grafos

Abstract

In this work we approach a little of the history of Leonard Euler, since it was responsible for the emergence of graph theory. In addition, some of the main concepts of graph theory will be presented. Moreover, we present a very important theorem of this area, the four-color theorem, which is used in planar graphs and until today it was not possible to demonstrate it without the help of the computer. The four-color theorem is very useful in coloring maps, the problem that led to this theorem was related to the coloring of a map. Finally, the main objective of this work is to demonstrate a simpler theorem than the four-color theorem, but more interesting since this theorem, the five-color theorem, can be proved by hand, without the aid of calculation hours of one computer. We conclude that although graph theory is not very well known, it is of great importance and much used in our day to day life.