A Tverberg-type result on multicolored simplices
János Pach · Computational Geometry · 1998
Let P1, P2,…, Pd+1 be pairwise disjoint n-element point sets in general position in d-space. It is shown that there exist a point O and suitable subsets Qi ⊆ Pi (i = 1, 2,…, d + 1) such that Qi ≥ cdPi, an every d-dimensional simplex with exactly one vertex in each Qi contains Q in its interior. Here cd is a positive constant depending only on d.