Generalized subgraph-restricted matchings in graphs Original Research Article

For a graph property image, we define a image-matching as a set M of disjoint edges such that the subgraph induced by the vertices incident to M has property image. Previous examples include strong/induced matchings and uniquely restricted matchings. We explore the general properties of image-matchings, but especially the cases where image is the property of being acyclic or the property of being disconnected. We consider bounds on and the complexity of the maximum cardinality of a image-matching and the minimum cardinality of a maximal image-matching.