More Colourful Simplices

We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each set. This improves the known lower bounds for all d ≥ 4. Keywords Colourful simplicial depth · Colourful Carathéodory theorem · Discrete geometry

• Type: Journal
• Year: 2011
• Where: DCG
• Authors: Antoine Deza, Tamon Stephen, Feng Xie
• Keywords: Colourful Simplicial Depth, Computer Graphics, Convex Hull, DCG 2011, Lower Bounds