55 citations · 124 across the 16 of their papers we have counts for
9 papers · 1 filter
Unique Triangulated 1-Planar Graphs
Franz J. Brandenburg
It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, whic…
Embedding 1-Planar Graphs in Ten Pages
Franz J. Brandenburg
Every planar graph has a 4-page book embedding and this bound is tight. We show that every 1-planar graph, which is a graph that admits a drawing with at most one crossing per edge…
On Optimal Beyond-Planar Graphs
Franz J. Brandenburg
A graph is beyond-planar if it can be drawn in the plane with a specific restriction on crossings. Several types of beyond-planar graphs have been investigated, such as k-planar if…
Fan-Crossing Free Graphs and Their Relationship to other Beyond-Planar Graphs
Franz J. Brandenburg
A graph is \emph{fan-crossing free} if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the ot…
On Fan-Crossing Graphs
Franz J. Brandenburg
A fan is a set of edges with a single common endpoint. A graph is fan-crossing if it admits a drawing in the plane so that each edge is crossed by edges of a fan. It is fan-planar…
A Note on IC-Planar Graphs
Christian Bachmaier, Franz J. Brandenburg, Kathrin Hanauer
A graph is IC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share no common end vertex. IC-planarity speci…
Recognizing IC-Planar and NIC-Planar Graphs
Franz J. Brandenburg
We prove that triangulated IC-planar and NIC-planar graphs can be recognized in cubic time. A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge.…
Path-Additions of Graphs
Franz J. Brandenburg, Alexander Esch, Daniel Neuwirth
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are jus…
Recognizing Optimal 1-Planar Graphs in Linear Time
Franz J. Brandenburg
A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. We show that op…