12 citations · 57 across the 39 of their papers we have counts for
7 papers · 1 filter
Beyond-Planarity: Density Results for Bipartite Graphs
Patrizio Angelini, Michael A. Bekos, Michael Kaufmann +2
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with…
On Vertex- and Empty-Ply Proximity Drawings
Patrizio Angelini, Steven Chaplick, Felice De Luca +7
We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equ…
3D Visibility Representations of 1-planar Graphs
Patrizio Angelini, Michael A. Bekos, Michael Kaufmann +1
We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parall…
Hierarchical Partial Planarity
Patrizio Angelini, Michael A. Bekos
In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they ap…
Universal Slope Sets for 1-Bend Planar Drawings
Patrizio Angelini, Michael A. Bekos, Giuseppe Liotta +1
We describe a set of slopes that are universal for 1-bend planar drawings of planar graphs of maximum degree ; this establishes a new upper bound of on the 1-b…
On the Relationship between -Planar and -Quasi Planar Graphs
Patrizio Angelini, Michael A. Bekos, Franz J. Brandenburg +6
A graph is -planar if it can be drawn in the plane such that no edge is crossed more than times. A graph is -quasi planar if it can be drawn in…
1-Fan-Bundle-Planar Drawings of Graphs
Patrizio Angelini, Michael A. Bekos, Michael Kaufmann +2
Edge bundling is an important concept heavily used for graph visualization purposes. To enable the comparison with other established near-planarity models in graph drawing, we form…