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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, June 21, 2016, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Patrick Schnider

Given a complete geometric graph, a set of pairwise crossing edges is called a crossing family. A result from 1990 states that every complete geometric graph on n vertices contains a crossing family of size \sqrt{n/12}. In some applications where this result is used, it is however not necessary that the edges actually cross, but only that their endpoints lie "niecly" in some sense. This can be made more precise by the definition of *spoke sets*: A spoke set is a set of lines through a point set such that in each unbounded region of the induced line arrangement there is at least one point of the point set. It is not to hard to see that this is a generalization of crossing families, in the sense that each crossing family of size k induces a spoke set of size k. We show that every point set contains a spoke set of size \sqrt{n/8}.

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

Previous talks by year: 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