A Combinatorial Property of Points and Balls, a Colored Version

Any finite set X ⊂ Rd colored with d+3 2 colors, contains a rainbow subset Y ⊂ X, such that any ball that contains Y contains a positive fraction of the points of X. The bound on the number of colors is tight.

• Type: Journal
• Year: 2007
• Where: DCG
• Authors: Maria N. Prodromou
• Keywords: Ball, DCG 2007, Rainbow