EFL segment conjecture: Let be a set of segments such that every pair has at most one point in common. Then, has an EFL coloring with colors.
The EFL segment conjecture is true in general: it can be applied to segments built on planar graphs.
Through a proof by Induction, the conjecture can be first proved for the base case. Then, by successively picking a segment that intersects a segment whose intersection points are already colored (starting with an arbitrary assignment of colors to intersection points of segments), an EFL coloring can be achieved--with all intersection points of colored.