The inducibility of complete bipartite graphs

For any s ≥ 1 and t ≥ ( S 2 ), we prove that among all graphs with n vertices the graph that contains the maximal number of induced copies of K t , t + s for any fixed s ≥ 1 and t ≥ ( s 2 ) is K ( n /2)+α( n /2)‐α for some function α = o ( n ). We show that this is not valid for t < ( s 2 ). Analogous results for complete multipartite graphs are also obtained.