Let G be a simple planar graph on 13 vertices. Prove that at least one of G and its complement G is not planar.
Can we say that: e<=3n-6 , where n = number of vertices $n(n-1)/2$ is the total number of edges in graph. Thus let's say that n = 5 , if we substitute it to $n(n-1)/2=e<=3n-6$ we will get that $10<=9$ which is not right. Actually we should substitude 13 i think to formula described before. From this point if G isn't planar , then G complement isn't planar as well? Is it possible to show it in this way?