## 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: Tuesday, June 30, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Otfried Cheong (Korea Advanced Institute of Science and Technology - KAIST, Daejeon, South Korea)

## Lines pinning lines

A line $\ell$ is a transversal to a family $F$ of convex polytopes in $\R^3$ if it intersects every member of $F$. If, in addition, $\ell$ is an isolated point of the space of line transversals to $F$, we say $F$ is a pinning of $\ell$. We show that any minimal pinning of a line by polytopes in $\R^3$ such that no face of a polytope is coplanar with the line has size at most eight. If in addition the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.

Information for students and suggested topics for student talks

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