Bichromatic and Equichromatic Lines in 2 and 2

Let G and R each be a finite set of green and red points, respectively, such that |G|=n, |R|=n-k, GR=, and the points of GR are not all collinear. Let t be the total number of lines determined by GR. The number of equichromatic lines (a subset of bichromatic) is at least (t+2n+3-k(k+1))/4. A slightly weaker lower bound exists for bichromatic lines determined by points in ^sup 2^. For sufficiently large point sets, a proof of a conjecture by Kleitman and Pinchasi is provided. A lower bound of (2t+14n-k(3k+7))/14 is demonstrated for bichromatic lines passing through at most six points. Lower bounds are also established for equichromatic lines passing through at most four, five, or six points.[PUBLICATION ABSTRACT]