Every planar graph with nine points has a nonplanar complement

In a complete graph every two points are joined by a line (are adjacent). A complete graph with n points is denoted by Kn> Let G be a graph with n points considered as a subgraph of Kn. The complement G of G is the graph obtained by removing all lines of G fromi£n. The following problem was stated by Harary [2 ] : What is the least integer n such that every graph G with n points or its complement G is nonplanar? Harary [3] observed that n^ll. I t is readily seen that n>8. In this note we shall outline the proof that n = 9, verifying a conjecture of J. L. Self ridge.