Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, March 15, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Marek Sulovský

Lower bounds for the rectilinear crossing number

We address the following question: What is the minimal number of crossings (denoted by crr(K_n)) in a straight-line drawing of K_n in the plane? This has been studied in recent years and the currently best asymptotic bounds for crr(K_n) are: 0.379 (n \choose 4) \leq crr(K_n) \leq 0.381 (n \choose 4). The talk will summarize two recent results, [1] and [2], giving lower bounds on rectilinear crossing number via proving that minimizing examples have a triangular convex hull, and for configurations with this property giving lower bounds on the number of (\leq k)-sets. The lower bound on the crossing number immediately follows from the lower bound on (\leq k)-sets.

[1] Aichholzer, Garcia, Orden, Ramos: On the structure of sets attaining rectilinear crossing number (Proc. 22th European Workshop on Computational Geometry EuroCG '06, pages 43-46).
[2] Abrego, Balogh, Fernandez-Merchant, Leanos, Salazar: On k-pseudoedges in generalized configurations and the pseudolinear crossing number of Kn (submitted).

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login