Given two graphs H and F, the maximum possible number of copies of H in
an F-free graph on n vertices is denoted by ex(n,H,F). We investigate the
function ex(n,H,kF), where kF denotes k vertex disjoint copies of a fixed
graph F. Our results include cases when F is a complete graph, cycle or a
complete bipartite graph.Comment: 18 pages. There was a wrong statement in the first version, it is
corrected no