## 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, May 29, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Gábor Fejes Tóth (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary)

## Shortest path among circles

Given a packing of open unit circles, any two points lying outside the circles at distance $d$ from one another can be connected by a path evading the circles and having length at most ${2\pi\over\sqrt{27}}(d-2)+\pi$. This bound cannot be improved for values of the form $2(k\sqrt3+1)$. Can a packing of incongruent circles with radii at most 1 force us to a greater detour? The answer is yes, but concerning this problem we have to be satisfied with weaker upper and lower bounds for the length of the shortest path.

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