Problem-solving techniques in infinite graphs

• Ano de defesa: 2024
• Autor(a) principal: Real, Lucas Silva Sinzato
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Edge-ends; End spaces; Espaços de extremidades; Extremidades via arestas; Grafos infinitos; Infinite graphs; Partições não amigáveis; Unfriendly partition
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-14052024-161415/

The study of infinite graphs consists in a singular area from graph theory. In general, its problems cannot be approached by counting principles or optimizing algorithms, typical tools from finite combinatorics. In fact, a sort of arguments that support proofs in infinite graph theory are inherited from other branches of mathematics, mainly those in which the notion of infinite itself is a matter of study. Regarding that, this work lies in the intersection between graph theory, set theory and topology, where some problems from first area will be analysed under a viewpoint of the others. With some special depth, we will study the unfriendly partition conjecture and its state of art, as well as the notion of ends in infinite graphs and their applications. Incidentally, besides revisiting the literature concerning these discussions, this dissertation contributes original results.