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

Date and Time: Thursday, April 09, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Meghana M. Reddy

Simple Topological Drawings of k-Planar Graphs

Every graph that admits a topological drawing also admits a simple topological drawing. It is easy to observe that every 1-planar graph admits a 1-plane simple topological drawing. It has been shown that 2-planar graphs and 3-planar graphs also admit 2-plane and 3-plane simple topological drawings respectively. However, nothing has been proved for simple topological drawings of k-planar graphs for k > 3. In fact, it has been shown that there exist 4-planar graphs which do not admit a 4-plane simple topological drawing, and the idea can be extended to k-planar graphs for k > 4. We prove that there exists a function f : N -> N such that every k-planar graph admits an f(k)-plane simple topological drawing for all k > 3. This answers a question posed by Schaefer. This is joint work with Chih-Hung Liu and Csaba D. Tóth.

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