1. ## Upper Bound Theorem

The converse of the Upper Bound Theorem would state that a graph which satisfies the inequality $e \leq { \frac{n (v-2)}{n-2}$ is planar.

This converse is not true as seen in picture.

Verify that the inequality $e \leq { \frac{n (v-2)}{n-2}$ is true for this graph. Once done, use the inside-outside algorithm to show that the graph is actually non-planar.

2. e = edges
v = vertices

but what is n?

3. perhaps it stand for number of points.

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