Generalized subgraph-restricted matchings in graphs

Abstract: For a graph property , we define a -matching as a set M of disjoint edges such that the subgraph induced by the vertices incident to M has property . Previous examples include strong/induced matchings and uniquely restricted matchings. We explore the general properties of -matchings, but especially the cases where 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 -matching and the minimum cardinality of a maximal -matching. [Copyright &y& Elsevier]