A survey on graph drawing beyond planarity

W Didimo, G Liotta, F Montecchiani - ACM Computing Surveys (CSUR), 2019 - dl.acm.org
Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and
studies geometric representations of nonplanar graphs in terms of forbidden crossing …

The density of fan-planar graphs

M Kaufmann, T Ueckerdt - arXiv preprint arXiv:1403.6184, 2014 - arxiv.org
A topological drawing of a graph is fan-planar if for each edge $ e $ the edges crossing $ e $
form a star and no endpoint of $ e $ is enclosed by $ e $ and its crossing edges. A fan …

Nonplanar Graph Drawings with k Vertices per Face

C Binucci, G Di Battista, W Didimo, SH Hong… - … Workshop on Graph …, 2023 - Springer
The study of nonplanar graph drawings with forbidden or desired crossing configurations
has a long tradition in geometric graph theory, and received an increasing attention in the …

Simple k-planar graphs are simple (k+ 1)-quasiplanar

P Angelini, MA Bekos, FJ Brandenburg… - Journal of Combinatorial …, 2020 - Elsevier
A simple topological graph is k-quasiplanar (k≥ 2) if it contains no k pairwise crossing
edges, and k-planar if no edge is crossed more than k times. In this paper, we explore the …

[HTML][HTML] 1-fan-bundle-planar drawings of graphs

P Angelini, MA Bekos, M Kaufmann… - Theoretical Computer …, 2018 - Elsevier
Edge bundling is an important concept, heavily used for graph visualization purposes. To
enable the comparison with other established nearly-planarity models in graph drawing, we …

Simplifying non-simple fan-planar drawings

B Klemz, K Knorr, MM Reddy, F Schröder - International Symposium on …, 2021 - Springer
A drawing of a graph is fan-planar if the edges intersecting a common edge a share a vertex
A on the same side of a. More precisely, orienting e arbitrarily and the other edges towards A …

Fan-planar graphs

MA Bekos, L Grilli - Beyond Planar Graphs: Communications of NII Shonan …, 2020 - Springer
A fan-planar graph is a graph that admits a drawing, in which each edge can cross only
edges with a common endvertex, and this endvertex is on the same side of the edge. Hence …

Simplifying non-simple fan-planar drawings

B Klemz, K Knorr, M Reddy, F Schröder - Journal of Graph Algorithms and …, 2023 - jgaa.info
A drawing of a graph is fan-planar if the edges intersecting a common edge $ a $ share a
vertex $ A $ on the same side of $ a $. More precisely, orienting $ a $ arbitrarily and the …

Graphs Drawn with Some Vertices per Face: Density and Relationships

C Binucci, G Di Battista, W Didimo, V Dujmović… - IEEE …, 2024 - ieeexplore.ieee.org
Graph drawing beyond planarity is a research area that has received an increasing attention
in the last twenty years, driven by the necessity to mitigate the visual complexity inherent in …

On the Relationship Between k-Planar and k-Quasi-Planar Graphs

P Angelini, MA Bekos, FJ Brandenburg… - … -Theoretic Concepts in …, 2017 - Springer
A graph is k-planar (k ≥ 1)(k≥ 1) if it can be drawn in the plane such that no edge is
crossed k+ 1 k+ 1 times or more. A graph is k-quasi-planar (k ≥ 2)(k≥ 2) if it can be drawn …