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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…
Optimizing Symbol Visibility through Displacement
Bernd Gärtner, Vishwas Kalani, Meghana M. Reddy +3
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positi…
Using SAT to study plane Hamiltonian substructures in simple drawings
Helena Bergold, Stefan Felsner, Meghana M. Reddy +1
In 1988 Rafla conjectured that every simple drawing of a complete graph contains a plane, i.e., non-crossing, Hamiltonian cycle. The conjecture is far from being resolved. Th…
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…