Given $n$ lines, no two of which are parallel and no more than two intersect at the same point. Construct a graph with the intersection of lines as vertices and the line segments as edges. Prove or disprove that this graph is Hamiltonian.
I checked this for many graphs of different sizes and in every case, I could find a Hamiltonian cycle. I know that for n lines, the number of vertices will be n(n-1)/2 and edges n(n-2). I have no clue how to use this information and how to proceed further.