1 citations · 1 across the 13 of their papers we have counts for
14 papers
What induces plane structures in complete graph drawings?
Alexandra Weinberger, Ji Zeng
This paper considers the task of connecting points on a piece of paper by drawing a curve between each pair of them. Under mild assumptions, we prove that many pairwise disjoint cu…
Grounded String Representations of Series-Parallel Graphs without Transitive Edges
Sabine Cornelsen, Jan Kratochvíl, Miriam Münch +3
In a {\em grounded string representation} of a graph there is a horizontal line and each vertex is represented as a simple curve below with one end point on su…
Characterizing and Recognizing Twistedness
Oswin Aichholzer, Alfredo García, Javier Tejel +2
In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills…
On -planar Graphs without Short Cycles
Michael A. Bekos, Prosenjit Bose, Aaron Büngener +6
We study the impact of forbidding short cycles to the edge density of -planar graphs; a -planar graph is one that can be drawn in the plane with at most crossings per edg…
On the rectilinear crossing number of complete balanced multipartite graphs and layered graphs
Ruy Fabila-Monroy, Rosna Paul, Jenifer Viafara-Chanchi +1
A rectilinear drawing of a graph is a drawing of the graph in the plane in which the edges are drawn as straight-line segments. The rectilinear crossing number of a graph is the mi…
Different Types of Isomorphisms of Drawings of Complete Multipartite Graphs
Oswin Aichholzer, Birgit Vogtenhuber, Alexandra Weinberger
Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze s…
Drawings of Complete Multipartite Graphs Up to Triangle Flips
Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang +5
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended r…
Shooting Stars in Simple Drawings of
Oswin Aichholzer, Alfredo García, Irene Parada +2
Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every…
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…
Empty Triangles in Generalized Twisted Drawings of
Alfredo García, Javier Tejel, Birgit Vogtenhuber +1
Simple drawings are drawings of graphs in the plane or on the sphere such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect a…
Rotation systems and simple drawings in surfaces
Rosna Paul, Gelasio Salazar, Alexandra Weinberger
Every simple drawing of a graph in the plane naturally induces a rotation system, but it is easy to exhibit a rotation system that does not arise from a simple drawing in the plane…
Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs
Oswin Aichholzer, Alfredo García, Javier Tejel +2
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a sp…
Removing Popular Faces in Curve Arrangements
Phoebe de Nooijer, Soeren Terziadis, Alexandra Weinberger +4
A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate…
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…