Algoritmos eficientes para emparelhamentos desconexos em grafos cordais e grafos bloco - Masquio, Bruno; Pinto, Paulo; Szwarcfiter, Jayme (Anais do Encontro de Teoria da Computação (ETC), 2019)
Graph matching problems are well studied and bring great contributions to Graph Theory from both the theoretical and practical points of view. There are numerous studies for unrestricted and weighted/unweighted matchings. More recently, subgraph-restricted matchings have been proposed, which consider properties of the subgraph induced by the vertices of the matching. In this paper, we approach one of these new proposals, disconnected matching, which seeks to study maximum matching, such that the subgraph induced by the matching vertices is disconnected. We have described efficient algorithms to solve the problem for chordal graphs and block graphs based on a theoretical characterization.