Thread: Upper Bound Theorem

The converse of the Upper Bound Theorem would state that a graph which satisfies the inequality is planar.

This converse is not true as seen in picture.

Verify that the inequality is true for this graph. Once done, use the inside-outside algorithm to show that the graph is actually non-planar.

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