Emparelhamentos desconexos

• Autor(a) principal: Masquio, Bruno Porto
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/7663
• topic: Algorithms; Block Graphs; Disconnected Matching; Matching; Split Graphs; Chordal Graphs; Trees; Minimal separators; Algoritmos; Árvores; Emparelhamento; Emparelhamento Desconexo; Grafo Bloco; Grafo Split; Grafo Cordal; Separadores minimais; Grafos - Teoria; Algoritimos; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Graph matchings are problems that have been studied for a long time and which bring great contributions to Graph Theory from both the theoretical and practical points of view. As a tradition, there are numerous studies in this field for unrestricted and unweightedmatchings. Morerecently, subgraph-restrictedmatchingshavebeenproposed, which consider properties from the subgraph induced by the matching vertices. In this paper, we approach one of these new proposals, which are disconnected matchings, which seekstostudymatchingsanditscardinalities,suchthatthesubgraphinducedbymatching vertices is disconnected. We were able to solve the problem for simple classes of graphs like paths, cycles and complete. In addition, we obtained results for split graphs, trees, block graphs and chordal graphs. For these last three classes, we present a theoretical basis that includes theorems of characterizations, as well as three new algorithms. This paper also includes a fourth algorithm, which finds a maximum matching for block graphs in linear time