A Note on Empty Balanced Tetrahedra in Two colored Point sets in ℝ^3

02/25/2020

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by   José M. Díaz-Bañez, et al.

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Let S be a set of n red and n blue points in general position in ℝ^3. Let τ be a tetrahedra with vertices on 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 it contains two blue vertices and two red vertices. In this paper we show that S spans Ω(n^5/2) empty balanced tetrahedra.