A Note on Empty Balanced Tetrahedra in Two-colored Point sets in R3

Abstract Let S be a set of n red and n blue points in general position in R 3 . Let τ be a tetrahedron with vertices in S. We say that τ is empty if it does not contain any point of S in its interior. We say that τ is balanced if two of its vertices are blue, and two of its vertices are red. In this paper we show that S spans Ω ( n 5 / 2 ) empty balanced tetrahedra.