Minimal obstructions for 1‐immersions and hardness of 1‐planarity testing
VP Korzhik, B Mohar - Journal of Graph Theory, 2013 - Wiley Online Library
A graph is 1‐planar if it can be drawn on the plane so that each edge is crossed by no more
than one other edge (and any pair of crossing edges cross only once). A non‐1‐planar …
than one other edge (and any pair of crossing edges cross only once). A non‐1‐planar …
1-Planar graphs
Y Suzuki - Beyond Planar Graphs: Communications of NII Shonan …, 2020 - Springer
Topological graph theory discusses, in most cases, graphs embedded in the plane (or other
surfaces). For example, such plane graphs are sometimes regarded as the simplest town …
surfaces). For example, such plane graphs are sometimes regarded as the simplest town …
[HTML][HTML] Right angle crossing graphs and 1-planarity
A Right Angle Crossing Graph (also called a RAC graph for short) is a graph that has a
straight-line drawing where any two crossing edges are orthogonal to each other. A 1-planar …
straight-line drawing where any two crossing edges are orthogonal to each other. A 1-planar …
On the density of maximal 1-planar graphs
FJ Brandenburg, D Eppstein, A Gleißner… - … Symposium on Graph …, 2012 - Springer
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most
once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar …
once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar …
Parameterized complexity of 1-planarity
MJ Bannister, S Cabello, D Eppstein - … London, ON, Canada, August 12-14 …, 2013 - Springer
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-
planar drawing is a drawing in which each edge participates in at most one crossing. Since …
planar drawing is a drawing in which each edge participates in at most one crossing. Since …
[HTML][HTML] 1-planarity of complete multipartite graphs
J Czap, D Hudák - Discrete Applied Mathematics, 2012 - Elsevier
1-planarity of complete multipartite graphs - ScienceDirect Skip to main contentSkip to article
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1-planarity of graphs with a rotation system
C Auer, F Brandenburg, A Gleißner… - Journal of Graph …, 2015 - jgaa-v4.cs.brown.edu
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most
once. 1-planarity is known NP-hard, even for graphs of bounded bandwidth, pathwidth, or …
once. 1-planarity is known NP-hard, even for graphs of bounded bandwidth, pathwidth, or …
Long cycles and spanning subgraphs of locally maximal 1‐planar graphs
A graph is 1‐planar if it has a drawing in the plane such that each edge is crossed at most
once by another edge. Moreover, if this drawing has the additional property that for each …
once by another edge. Moreover, if this drawing has the additional property that for each …
[PDF][PDF] On properties of maximal 1-planar graphs
ON PROPERTIES OF MAXIMAL 1-PLANAR GRAPHS1 Page 1 Discussiones Mathematicae
Graph Theory 32 (2012) 737–747 doi:10.7151/dmgt.1639 ON PROPERTIES OF MAXIMAL 1-PLANAR …
Graph Theory 32 (2012) 737–747 doi:10.7151/dmgt.1639 ON PROPERTIES OF MAXIMAL 1-PLANAR …
Bar 1-visibility graphs and their relation to other nearly planar graphs
A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented
as horizontal segments (bars) in the plane so that its edges are all (resp. a subset of) the …
as horizontal segments (bars) in the plane so that its edges are all (resp. a subset of) the …