Teoria dos grafos: uma abordagem sobre o problema das quatro cores com alunos do 2° ano do ensino médio do Instituto Federal do Amapá

Abstract

The present work addresses the theme of graph theory, where the basic definitions, fundamental and important theorems for understanding the theme will be pointed out, in addition to the most famous problems that have stood out in the course of history in a succinct way, namely: The problem of the seven bridges of Königsberg which is the question of crossing certain seven bridges without repeating the passage through them once. Many people have tried to find a solution to this problem, but it was Leonard Euler who gave an answer to this challenge. The Four Colors Theorem, pointing from its origin, theorems and the main mathematicians who helped in the development of the four colors problem. Initially the problem of four colors started with the mathematician Francis Guthrie, studied by Alfred Bray Kemp and its refutation through the counterexample of Percy John Heawood. Which continued the proof of Percy John Heawood's Five Colors Theorem. Workshops on the subject were applied with IFAP High School students and, after an explanation of the initial ideas of the theory, some problems were proposed for the participants. The results indicate that addressing different topics, which do not require major prerequisites for their understanding, such as Graph Theory, combined with the use of dynamic mathematics software, such as Geogebra, enhances and streamlines the class, in addition to motivating the student in mathematics teaching-learning process.