Write down a proof that the n-cube cannot be realized as a planar graph for any n >=4.
I know I want to use the inequality of kF<=2E
and F=E-V+2 but I am not sure how to find the values.
A 4 cube has 16 nodes, and k = 3, so there are 48 edges, and 16 vertices. So there is 34 faces for it to be planar. But 102 is not less than 96 so a 4 cube is not planar.
Not so sure how to make this into a proof though. Any help would be much appreciated.