Points, Lines, Triangles and Graphs

You are given an integer $k$. You want to choose $n$ points on the plane and join some pairs of those points with line segments (let us call them edges), such that: - $n < 510$ - Any two points are distinct - No three points are collinear - The points have non-negative integer coordinates $\leq 10^9$. - No two edges (drawn line segments) intersect at a point which is not an endpoint of either edg