On Order Types of Systems of Segments in the Plane

Let r(n) denote the largest integer such that every family C of n pairwise disjoint segments in the plane in general position has r(n) members whose order type can be represented by points. Pach and T´oth gave a construction that shows r(n) < nlog 8/ log 9 [11]. They also stated that one can apply the Erd˝os-Szekeres theorem for convex sets in [10] to obtain r(n) > log16 n. In this note, we will show that r(n) > cn1/4 for some absolute constant c.

• Type: Journal
• Year: 2010
• Where: ORDER
• Authors: Andrew Suk
• Keywords: General Position, ORDER 2010, Order Type, Show