Detalhes bibliográficos
Ano de defesa: |
2021 |
Autor(a) principal: |
Phelipe Araujo Fabres |
Orientador(a): |
Marcelo Henriques de Carvalho |
Banca de defesa: |
Não Informado pela instituição |
Tipo de documento: |
Tese
|
Tipo de acesso: |
Acesso aberto |
Idioma: |
por |
Instituição de defesa: |
Fundação Universidade Federal de Mato Grosso do Sul
|
Programa de Pós-Graduação: |
Não Informado pela instituição
|
Departamento: |
Não Informado pela instituição
|
País: |
Brasil
|
Palavras-chave em Português: |
|
Link de acesso: |
https://repositorio.ufms.br/handle/123456789/4185
|
Resumo: |
McCuaig proved a generation theorem for braces, and used it as the principal induction tool to obtain a structural characterization of Pfaffian braces. A brace is minimal if deleting any edge results in a graph that is not a brace. From McCuaig’s brace generation theorem, we derive our main theorem that may be viewed as an induction tool for minimal braces. As an application, we prove that a minimal brace of order 2n has size at most 5n − 10, when n ≥ 6, and we provide a complete characterization of minimal braces that meets this upper bound. A similar work has already been done in the context of minimal bricks by Norine-Thomas wherein they deduce the main result from the brick generation theorem due to the same authors. Therefore, we built a definitive version, combining an alternative proof of Norine-Thomas’s theorem with our main theorem, for building minimal bricks and braces. |