A further generalization of the colourful Carathéodory theorem

Frédéric Meunier, Antoine Deza

Given $d+1$ sets, or colours, $S_1,S_2,...,S_{d+1}$ of points in ${\mathbb{R}}^d$, a {\em colourful} set is a set $S\subseteq {\bigcup }_i{S}_i$ such that $|S\cap S_i|\le 1$ for $i=1,..…