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Induced Decompositions of Graphs



We consider those graphs G that admit decompositions into copies of a fixed graph F, each copy being an induced subgraph of G. We are interested in finding the extremal graphs with this property, that is, those graphs G on n vertices with the maximum possible number of edges. We discuss the cases where F is a complete equipartite graph, a cycle, a star, or a graph on at most four vertices.