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2010

On Order Types of Systems of Segments in the Plane

9 years 4 months ago
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.
Andrew Suk
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where ORDER
Authors Andrew Suk
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