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...
Seog-Jin Kim, Kittikorn Nakprasit, Michael J. Pels...
Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices ...
We prove a lower bound of 0.3288 n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
Let S be a set of r red points and b = r +2 blue points in general position in the plane. A line determined by them is said to be balanced if in each open half-plane bounded by th...
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...