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

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, April 10, 2018, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Pavel Valtr (Charles University)

On the maximum crossing number

Research about edge crossings in graphs drawn in the plane is typically focused on minimization. In this talk, we consider MAXIMIZING the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a convex straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Joint work with Markus Chimani, Stefan Felsner, Stephen Kobourov, Torsten Ueckerdt and Alexander Wolff.

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