Forbidden Induced Bipartite Graphs

Given a fixed bipartite graph H, we study the asymptotic speed of growth of the number of bipartite graphs on n vertices which do not contain an induced copy of H. Whenever H contains either a,,cycle or the bipartite complement of a cycle, the speed of growth is 2(Omega(n6/5)). For every other bipartite graph except the path on seven vertices, we are able to find both upper and lower bounds of the form n(cn+o(n)). In many cases we are able to determine the correct value of C. (c) 2008 Wiley Periodicals, Inc. J Graph Theory 60: 219-241, 2009