Balanced 6-holes in linearly separable bichromatic point sets

We consider an Erdős type question on k-holes (empty k-gons) in bichromatic point sets. For a bichromatic point set S = R ∪ B , a balanced 2k-hole in S is spanned by k points of R and k points of B. We show that if R and B are linearly separable and | R | = | B | = n , then the number of balanced 6-holes in S is at least 1 15 n 2 − Θ ( n ) .