19 citations · 74 across the 43 of their papers we have counts for
8 papers · 1 filter
On weighted sums of numbers of convex polygons in point sets
Clemens Huemer, Deborah Oliveros, Pablo Pérez-Lantero +2
Let be a set of points in general position in the plane, and let be the number of convex -gons with vertices in that have exactly points of $S…
On the edge-vertex ratio of maximal thrackles
Oswin Aichholzer, Linda Kleist, Boris Klemz +2
A drawing of a graph in the plane is a thrackle if every pair of edges intersects exactly once, either at a common vertex or at a proper crossing. Conway's conjecture states that a…
On the 2-colored crossing number
Oswin Aichholzer, Ruy Fabila-Monroy, Adrian Fuchs +4
Let be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of is the minimum number of crossings between edges of the same color, taken over all p…
Inserting one edge into a simple drawing is hard
Alan Arroyo, Fabian Klute, Irene Parada +3
A {\em simple drawing} of a graph is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge in the complement o…
Graphs with large total angular resolution
Oswin Aichholzer, Matias Korman, Yoshio Okamoto +4
The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawi…
Minimal Representations of Order Types by Geometric Graphs
Oswin Aichholzer, Martin Balko, Michael Hoffmann +8
In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order ty…
Transformed flips in triangulations and matchings
Oswin Aichholzer, Lukas Andritsch, Karin Baur +1
Plane perfect matchings of points in convex position are in bijection with triangulations of convex polygons of size . Edge flips are a classic operation to perform local…
Flip distances between graph orientations
Oswin Aichholzer, Jean Cardinal, Tony Huynh +4
Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance…