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math.CO2025
Monotonically Decreasing the Number of Directed 3-Cycles via Edge-Flips?
David Bom, Florian Unger, Birgit Vogtenhuber
We investigate a combinatorial reconfiguration problem on oriented graphs, where a reconfiguration step (edge-flip) is the inversion of the orientation of a single edge. A recently…
math.CO2025
Crossing and non-crossing families
Todor Antić, Martin Balko, Birgit Vogtenhuber
For a finite set of points in the plane in general position, a \emph{crossing family} of size in is a collection of line segments with endpoints in that are pai…
math.CO2025
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…