MathDB

I've come across a challenging graph theory problem. Roughly translated, it goes something like this:
There are n lines drawn on a plane; no two lines are parallel to each other, and no three lines meet at a single point.
Those lines would partition the plane down into many 'area's. Suppose we select one point from each area. Also, should two areas share a common side, we connect the two points belonging to the respective areas with a line.
A graph consisted of points and lines will have been made. Find all possible 'n' that will make a hamiltonian circuit exist for the given graph

Problem Statement