Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, February 07, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Viola Mészáros (Univ. of Szeged, Charles Univ. Prague)

Alternating Paths in Bicolored Point Sets

It is a basic problem in geometric graph theory to decide which graphs can be drawn on a given point set with noncrossing straight-line edges. Eg. it is known that every outerplanar graph of n vertices can be drawn on any set of n points in general position in the plane. If the graph is a rooted tree, even the image of the root can be specified in advance and one can still find a proper embedding. We obtain new questions by considering colored point sets.

Problem (posed by Erdős around 1989): Determine or estimate the largest number l=l(n) such that, for every set of n red and n blue points on a circle, there exists a noncrossing alternating path consisting of l vertices. He showed that l(n)<=3/2*n+2. He conjectured that his configuration had been asymptotically extremal. Later this was disproved by Jan Kyncl, Janos Pach and Geza Toth. They conjecture that |l(n)-4/3*n|=o(n).

I'm going to present some of the previous results and my results related to the topic.

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

Previous talks by year:   2025  2024  2023  2022  2021  2020  2019  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