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## Orientations of Planar Graphs

### Stefan Felsner

Dartmouth

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Thursday, Sept. 25, 2008

007 Kemeny Hall, 4 pm

Tea 3:30 pm, 300 Kemeny Hall

**Abstract: **
We consider orientations of planar graphs, e.g., bipolar orientations, Schnyder woods and general alpha-orientations. To motivate their study we show some applications of these objects. Then we turn to counting problems and ask questions like: How many bipolar orientations can a planar graph on n vertices have? How many Schnyder woods of triangulations with n vertices exist? Regarding the first question we can only provide bounds but in the second case there is a closed formula and a bijective proof. If time allows we introduce a distributive lattice structure on alpha-orientations and explain some generalizations.

This talk will be accessible to graduate students.