ICS Theory Group

ICS 269, Fall 2000: Theory Seminar

Dec 8 2000:
A presentation based on "Triangles in Euclidean Arrangements," by S. Felsner and K. Kriegel, Discrete Computational Geometry 22 (1999), pp. 429-438.
Speaker: Javid Hüseynov, ICS, UC Irvine

The number of triangles in arrangements of lines and pseudolines has been the object of some research. While most of the results concern arrangements in the projective plane, this paper presents the results on the number of triangles in Euclidean arrangements of pseudolines. It presents another proof by the authors that a simple arrangement of n pseudolines contains at least n-2 triangles. The best possible bound of 2n/3 triangles in non-simple arrangements of n pseudolines is also presented in this paper.