Coloring axis-parallel rectangles

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r = 2, this answers a question of S. Smorodinsky [S06].

• Type: Journal
• Year: 2010
• Where: JCT
• Authors: János Pach, Gábor Tardos
• Keywords: Axis-parallel Rectangles, Color, JCT 2010