A quadratic lower bound for colourful simplicial depth

We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.

• Type: Journal
• Year: 2008
• Where: JCO
• Authors: Tamon Stephen, Hugh Thomas
• Keywords: Convex Hull, JCO 2008, Simplices