Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 21, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Stefan Felsner (TU Berlin)

Triangle Flip Graphs of Arrangements of Pseudolines and Pseudocircles

We consider triangle flips in arrangements. For simple Euclidean arrangements of n pseudolines it is known that there are at least n-2 triangles. We show that the connectivity of the flip graph equals its minimum degree. For the proof we introduce the class of shellable line arrangements, which serve as destination objects for the construction of disjoint paths. Shellable arrangements are elements of flip graphs of line arrangements which are the vertices of a polytope These polytopes form clusters of good connectivity in the flip graph of pseudolines. In the case of intersecting arrangements of pseudocircles we discuss the number of triangles. Finally we show that the triangle flip graph is connected. In the proof cylindrical intersecting arrangements of pseudocircles play a special role.

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