2 citations · 4 across the 6 of their papers we have counts for
7 papers
Flip Graph Connectivity for Arrangements of Pseudolines and Pseudocircles
Yan Alves Radtke, Stefan Felsner, Johannes Obenaus +3
Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer…
Compatible Spanning Trees in Simple Drawings of
Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer +6
For a simple drawing of the complete graph , two (plane) subdrawings are compatible if their union is plane. Let be the set of all plane spanning trees on…
Flipping Plane Spanning Paths
Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer +3
Let be a planar point set in general position, and let be the set of all plane straight-line paths with vertex set . A flip on a path …
Edge Partitions of Complete Geometric Graphs (Part 2)
Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber +5
Recently, the second and third author showed that complete geometric graphs on vertices in general cannot be partitioned into plane spanning trees. Building up on this wor…
Edge Partitions of Complete Geometric Graphs (Part 1)
Johannes Obenaus, Joachim Orthaber
In this paper, we disprove the long-standing conjecture that any complete geometric graph on vertices can be partitioned into plane spanning trees. Our construction is bas…
Plane Spanning Trees in Edge-Colored Simple Drawings of
Oswin Aichholzer, Michael Hoffmann, Johannes Obenaus +5
Károlyi, Pach, and Tóth proved that every 2-edge-colored straight-line drawing of the complete graph contains a monochromatic plane spanning tree. It is open if this statement gene…
The Tree Stabbing Number is not Monotone
Wolfgang Mulzer, Johannes Obenaus
Let be a set of points and be a spanning tree of . The \emph{stabbing number} of is the maximum number of intersections any line in the plane…