Before revision:  The best previous bound on the number of edges was O(n^{3/2}), proved by Babai,  Erdos, Chung, Graham, and Spencer in 1982.  vertices and edges that contains induced copies of every n-vertex planar graph.
After revision:  The best previous bound on the number of edges was O(n^{3/2}), proved by Babai, Chung, Erdos, Chung, Graham, and Spencer in 1982. vertices and edges that contains induced copies of every n-vertex planar graph.