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math.CO2023
The Density Formula: One Lemma to Bound Them All
Michael Kaufmann, Boris Klemz, Kristin Knorr +3
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 t…
math.CO2023
The Number of Edges in Maximal 2-planar Graphs
Michael Hoffmann, Meghana M. Reddy
A graph is -planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal -planar if no…