## 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, February 27, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Sonoko Moriyama (Tohoku University)

## Minimal non-orientable matroids of rank three

Minimal non-orientable matroids have been investigated to characterize orientable matroids. The Fano matroid and the MacLane matroid are well-known minimal non-orientable matroids of rank $3$. A natural question is whether there exists a minimal non-orientable matroid of every rank $r$ with $m$ elements. In this talk, we give an answer to the question in rank $3$ that for every $m \geq 7$, there exists a minimal non-orientable matroid of rank $3$ with $m$ elements. To prove this statement, we construct two new infinite families of minimal non-orientable matroids of rank $3$.

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