6 papers
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…
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…
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…