Grafos: definições elementares e método probabilístico

• Ano de defesa: 2015
• Autor(a) principal: Martins, Gizele Justino Diniz
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Mestrado Profissional em Matemática; UFPB
• Palavras-chave em Português: Grafos; Graph; Número cromático; Número de Ramsey; Probabilidade; Variável aleatória; Método probabilístico; Chromatic number; Number of Ramsey; Probability; Random variable; Probabilistic methods; MATEMATICA::MATEMATICA APLICADA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7566

In this work we study the graph theory, which although it is somewhat widespread content, including academia is extremely important for solving many mathematical problems and physical models. Moreover, this theme can be found in applications in several areas, including quote: computer, electrical, genetic. We adopt the bibliographic research and exploratory research to deal with the issue at hand, trying to de ne and clarify the aforesaid theory, but also contribute to its spread, which enables members of the basic and higher education have a contact with such an important and fruitful know, since elementary considerations graphs brings us closer to scienti c research. We alternate concepts and statements of lemmas and theorems to solve problems. We use simple language, so that a high school student can understand, without, however, distancing us from mathematical rigor. In time, we present the four color theorem the number of Ramsey, with detailed statements of the latter result. Finally, we use concepts and purely combinatorial results and probability, using the probabilistic method to prove the existence of graphs with certain properties that are di cult construction and, through this evidence, get other desired graph.