On The Number of Subgraphs of Prescribed Type of Planar Graphs With A Given Number of Vertices

For a planar graph H and a positive integer n we study the maximal number f = f(n, H ), such that there exists a planar graph on n vertices containing f subgraphs isomorphic to H . We determine f(n, H ) precisely if H is either a complete bipartite (planar) graph or a maximal planar graph without triangles that are not faces, and estimate f(n, H ) for every maximal planar graph H .