On Order Types of Systems of Segments in the Plane

作者：Suk Andrew^*

来源：Order, 2010, 27(1): 63-68.

DOI：10.1007/s11083-010-9138-4

• Order types
• Convex sets
• Segments

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 Toth gave a construction that shows r(n) < n (log8/log9) (Pach and Toth 2009). They also stated that one can apply the Erdos-Szekeres theorem for convex sets in Pach and Toth (Discrete Comput Geom 19:437-445, 1998) to obtain r(n) > log(16) n. In this note, we will show that r(n) > cn (1/4) for some absolute constant c.

• 出版日期2010-3