Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, February 22, 2022, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Meghana M. Reddy
A drawing of a graph is fan-planar if the edges intersecting a common edge $a$ share a vertex $A$ on the same side of $a$. More precisely, orienting $e$ arbitrarily and the other edges towards $A$ results in a consistent orientation of the crossings. So far, fan-planar drawings have only been considered in the context of simple drawings, where any two edges share at most one point, including endpoints. We show that every non-simple fan-planar drawing can be redrawn as a simple fan-planar drawing of the same graph while not introducing additional crossings, thereby answering an open problem posed by Kaufmann and Ueckerdt in 2014. Combined with previous results on fan-planar drawings, this yields that $n$-vertex-graphs having such a drawing can have at most $6.5n$ edges and that the recognition of such graphs is NP-hard. This is joint work with Boris Klemz, Kristin Knorr and Felix Schröder.
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