A Note on Empty Balanced Tetrahedra in Two colored Point sets in ${\mathbb{R}}^3$

José M. Díaz-Bañez, Ruy Fabila-Monroy, Jorge Urrutia

Let $S$ be a set of $n$ red and $n$ blue points in general position in ${\mathbb{R}}^3$. Let $\tau$ be a tetrahedra with vertices on $S$. We say that $\tau$ is \emph{empty} if it does not…