Forbidding Multiple Copies of Forestable Graphs

The Turán number of a graph H is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. We call a graph H forestable if it is cyclic, bipartite, and contains a vertex v such that H[V∖ v] is a forest. For a forestable graph H , we determine ex(n,k· H) exactly as a function of ex(n,H) . This is related to earlier work of the authors on the Turán numbers for equibipartite forests.