摘要
A property of graphs is a non-empty isomorphism-closed class of simple graphs. If are properties of graphs, the property is the class of all graphs that have a vertex partition such that for . The property is the class of all graphs that have an edge partition such that for . A property which is not the class of all graphs is said to be reducible over a set of properties if there exist properties such that . is decomposable over if . We study questions of the form: If is reducible (decomposable) over , does it follow that is reducibe (decomposable) over ?