Drawing Graphs with Right Angle Crossings
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A characterization of complete bipartite RAC graphs
Information Processing Letters
Graphs that admit right angle crossing drawings
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
The straight-line RAC drawing problem is NP-hard
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On the size of graphs that admit polyline drawings with few bends and crossing angles
GD'10 Proceedings of the 18th international conference on Graph drawing
The quality ratio of RAC drawings and planar drawings of planar graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Vertex angle and crossing angle resolution of leveled tree drawings
Information Processing Letters
Density of straight-line 1-planar graph drawings
Information Processing Letters
On the density of maximal 1-planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Testing maximal 1-planarity of graphs with a rotation system in linear time
GD'12 Proceedings of the 20th international conference on Graph Drawing
Parameterized complexity of 1-planarity
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system
Theoretical Computer Science
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A Right Angle Crossing Graph (also called 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 graph is a graph that has a drawing where every edge is crossed at most once. We study the relationship between RAC graphs and 1-planar graphs in the extremal case that the RAC graphs have as many edges as possible. It is known that a maximally dense RAC graph with n3 vertices has 4n --- 10 edges. We show that every maximally dense RAC graph is 1-planar. Also, we show that for every integer i such that i≥0, there exists a 1-planar graph with n=8+4i vertices and 4n --- 10 edges that is not a RAC graph.