4 papers · 1 filter
Edge densities of drawings of graphs with one forbidden cell
Benedikt Hahn, Torsten Ueckerdt, Birgit Vogtenhuber
A connected topological drawing of a graph divides the plane into a number of cells. The type of a cell is the cyclic sequence of crossings and vertices along the boundary walk…
Number of Edges in 3-Connected Graphs with Cyclic Neighborhoods
Samuel Schneider, Torsten Ueckerdt
Chernyshev, Rauch and Rautenbach [Discrete Math., 2025] introduce forest cuts, i.e., vertex separators that induce a forest. They conjecture that, similar to a result by Chen and Y…
Crossing Number of 3-Plane Drawings
Miriam Goetze, Michael Hoffmann, Ignaz Rutter +1
We study 3-plane drawings, that is, drawings of graphs in which every edge has at most three crossings. We show how the recently developed Density Formula for topological drawings…
A Note on Polychromatic Colorings of Shift-Chains
Torsten Ueckerdt
We popularize the question whether, for large enough, all -uniform shift-chain hypergraphs are properly -colorable. On the other hand, we show that for every some …