ÍâÍøÌìÌÃ

Given a graph H and a family of graphs F, we define the generalized Turan number ex(n,H,F) to be the maximum number of copies of H in an F-free graph on n vertices.Ìý We prove a Ìý``stability'' type result for generalized Turan problems which relates the generalized Turan number ex(n,H,F) Ìýto the classical Turan number ex(n,F) whenever H is a tree.ÌýWe discuss some applications of this result, as well as some related work around the rational exponents conjecture for general graphs H.Ìý Joint work with Sean English.