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

Date and Time: Tuesday, December 12, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Meghana M. Reddy

The Density Formula: One Lemma to Bound Them All

We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. The Density Formula can be seen as a generalization of Euler's formula for Beyond-Planar graphs. We demonstrate its capability by providing a few applications: we prove tight upper bounds on the edge density of various beyond-planar graph classes, including so-called k-planar graphs with k=1,2, fan-crossing/fan-planar graphs, RAC-graphs, and some more. In some cases, the Density Formula can also be used to characterize graphs with optimal density or to obtain tight lower bound constructions. This is joint work with Michael Kaufmann, Boris Klemz, Kristin Knorr, Felix Schroder and Torsten Ueckerdt.

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