Subgraph Packing — A Survey

The research on factors of graphs concentrated mostly on factors satisfying certain local degree conditions, like regular factors or factors with degrees within prescribed intervals. More recently, also other kinds of factors have been investigated. Here we survey results on factors with prescribed components. Let F be a family of graphs. A graph G is said to have an F — factor if it has a factor each component of which is isomorphic to a member of family F The F — factor problem is to decide whether a given graph G admits an F — factor. The F — packing problem is to find a subgraph of maximum order which admits an F — factor.