5 papers
A Simplified Proof for the Edge-Density of 4-Planar Graphs
Aaron Büngener
A graph on vertices drawn in the plane such that each edge is crossed at most four times has at most edges -- this result, proven by Ackerman, is outstanding in…
A first view on the density of 5-planar graphs
Aaron Büngener, Jakob Franz, Michael Kaufmann +1
A key concept for many graph layout algorithms is planarity, a graph property that allows to draw vertices and edges crossing-free in the plane. Important is the generalization to…
Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs
Aaron Büngener, Michael Kaufmann
The classical Crossing Lemma by Ajtai et al.~and Leighton from 1982 gave an important lower bound of for the number of crossings in any drawing of a given graph…
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…
Min--planar Drawings of Graphs
Carla Binucci, Aaron Büngener, Giuseppe Di Battista +7
The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. On…