N red points and N blue points placed on a sphere. Each R point is connected to each B point via a segment of a great circle. S(N) = minimal number of intersection points possible. I(4) = 4 ? I(5) = ?
Ah, I see. Each R point must be connected not merely to some B point, but to each B point, and conversely. So the placement I proposed does indeed meet this condition, but the number of intersection points in my case is uncountable.