5 papers · 1 filter
Two-edge-connected (not necessarily spanning) subgraphs and polyhedra
Justus Bruckamp, Markus Chimani, Martina Juhnke
Given a graph , we study the -edge-connected subgraph polytope , which is given by the convex hull of the incidence vectors of all -edge-connected subgr…
A Systematic Approach to Crossing Numbers of Cartesian Products with Paths
Zayed Asiri, Ryan Burdett, Markus Chimani +3
Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the est…
The Price of Upwardness
Patrizio Angelini, Therese Biedl, Markus Chimani +8
Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyon…
Crossing Numbers of Beyond Planar Graphs Re-revisited: A Framework Approach
Markus Chimani, Torben Donzelmann, Nick Kloster +3
Beyond planarity concepts (prominent examples include k-planarity or fan-planarity) apply certain restrictions on the allowed patterns of crossings in drawings. It is natural to as…
Exact Minimum Weight Spanners via Column Generation
Fritz Bökler, Markus Chimani, Henning Jasper +1
Given a weighted graph , a minimum weight -spanner is a least-weight subgraph that preserves minimum distances between all node pairs up to a factor of . Th…