Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, November 10, 2020, 12:15 pm
Duration: 30 minutes
Location: Zoom: conference room
Speaker: Michael Hoffmann
A star-simple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. When allowing empty lenses (a face in the arrangement induced by two edges that is bounded by a 2-cycle), two independent edges may cross arbitrarily many times in a star-simple drawing. We consider star-simple drawings of K_n with no empty lens. In this setting we prove an upper bound of 3((n-4)!) on the maximum number of crossings between any pair of edges. It follows that the total number of crossings is finite and upper bounded by n!. Joint work with Stefan Felsner, Kristin Knorr, and Irene Parada.
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