Transversal numbers of translates of a convex body

Let F be a family of translates of a fixed convex set M in Rn. Let (F) and (F) denote the transversal number and the independence number of F, respectively. We show that (F) (F) 8 (F) - 5 for n = 2 and (F) 2n-1nn (F) for n 3. Furthermore, if M is centrally symmetric convex body in the plane, then (F) (F) 6 (F) - 3.

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Seog-Jin Kim, Kittikorn Nakprasit, Michael J. Pelsmajer, Jozef Skokan
• Keywords: DM 2006, Fixed Convex, Independence Number, Transversal Number