A Colored Version of Tverberg's Theorem
The main result of this paper is that given n red, n white, and n green points in the plane, it is possible to form n vertex-disjoint triangles Δ 1 ,…,Δ n in such a way that the Δ i has one one red, one white, and one green vertex for every i = 1,…, n and the intersection of these triangles is nonempty.
Bárány, Imre and Larman, D. G., "A Colored Version of Tverberg's Theorem" (1990). Cowles Foundation Discussion Papers. 1179.