Milićević's cubic-curve conjecture for bichromatic point configurations

Let $n$ blue points, no three on a line, and $n$ red points disjoint from the blue points be given. Assume that every line through two blue points contains a red point. Milićević's conjecture. All $2n$ points lie on a cubic curve. The examples discussed include configurations on a reducible cubic, namely a conic together with a line, and on an irreducible cubic; the conjecture asserts that every such construction has this algebraic form.