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A Tverberg-type result on multicolored simplices

János Pach
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Abstract

Let $P_1, P_2,\ldots, P_{d+1}$ 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 $Q_i\subseteq P_i \; (i=1, 2, \ldots, d+1)$ such that $|Q_i|\geq c_d|P_i|$, and every $d$-dimensional simplex with exactly one vertex in each $Q_i$ contains $O$ in its interior. Here $c_d$ is a positive constant depending only on $d$.

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János Pach. 1996-03-08. A Tverberg-type result on multicolored simplices. https://arxiv.org/abs/math/9603211

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