I am reading about planar graphs from this site.
The complete bipartite graph K3,3 is not planar, since every drawing of K3,3contains at least one crossing. why? because K3,3 has a cycle which must appear in any plane drawing.
I am not able to get what cycle which must appear in any plane drawing has to do with edge crossing. Can't a cycle appear in plane drawing without crossing edges and thus letting the graph be planar? I must be missing something stupid.