55 citations · 124 across the 16 of their papers we have counts for
9 papers · 1 filter
Straight-line Drawings of 1-Planar Graphs
Franz J. Brandenburg
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawin…
Book Embeddings of k-Map Graphs
Franz J. Brandenburg
A map is a partition of the sphere into regions that are labeled as countries or holes. The vertices of a map graph are the countries of a map. There is an edge if and only if the…
Simple -Planar Graphs are Simple -Quasiplanar
Patrizio Angelini, Michael A. Bekos, Franz J. Brandenburg +8
A simple topological graph is -quasiplanar () if it contains no pairwise crossing edges, and -planar if no edge is crossed more than times. In this paper, we…
T-Shape Visibility Representations of 1-Planar Graphs
Franz J. Brandenburg
A shape visibility representation displays a graph so that each vertex is represented by an orthogonal polygon of a particular shape and for each edge there is a horizontal or vert…
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…
A Reduction System for Optimal 1-Planar Graphs
Franz J. Brandenburg
There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the give…
On the Book Thickness of 1-Planar Graphs
Md. Jawaherul Alam, Franz J. Brandenburg, Stephen G. Kobourov
In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called…
On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem
Franz J. Brandenburg
We establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they a…
Recognizing and Drawing IC-planar Graphs
Franz J. Brandenburg, Walter Didimo, William S. Evans +3
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-pl…