Inducibility of rainbow graphs

Fix k≥ 11 and a rainbow k-clique R. We prove that the inducibility of R is k!/(kᵏ-k). An extremal construction is a balanced recursive blow-up of R. This answers a question posed by Huang, that is a generalization of an old problem of Erd os and S\'os. It remains open to determine the minimum k for which our result is true. More generally, we prove that there is an absolute constant $C>0$ such that every k-vertex connected rainbow graph with minimum degree at least Clog k has inducibility k!/(kᵏ-k).