
Upper Bound Theorem
The converse of the Upper Bound Theorem would state that a graph which satisfies the inequality $\displaystyle e \leq { \frac{n (v2)}{n2} $ is planar.
This converse is not true as seen in picture.
Verify that the inequality $\displaystyle e \leq { \frac{n (v2)}{n2} $ is true for this graph. Once done, use the insideoutside algorithm to show that the graph is actually nonplanar.

e = edges
v = vertices
but what is n?

perhaps it stand for number of points.

could someone work out the inside outside algorithm? I'm stuck