Transversal numbers of translates of a convex body

Seog-Jin Kim, Kittikorn Nakprasit, Michael J. Pelsmajer, Jozef Skokan
2006 Discrete Mathematics  
Let F be a family of translates of a fixed convex set M in R n . 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) 2 n−1 n n (F) for n 3. Furthermore, if M is centrally symmetric convex body in the plane, then (F) (F) 6 (F) − 3.
doi:10.1016/j.disc.2006.05.014 fatcat:noo2ccgovnalrjws3bu5kpz5ra