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On RAC Drawings of Graphs with one Bend per Edge
[article]
2018
arXiv
pre-print
Preserved Fulltext
A k-bend right-angle-crossing drawing or (k-bend RAC drawing, for short) of a graph is a polyline drawing where each edge has at most k bends and the angles formed at the crossing points of the edges are ...
We also demonstrate that there exist infinitely many n-vertex 1-bend RAC graphs with exactly 5n-O(1) edges. ...
that admit polyline drawings, with few bends per edge, in which the angles formed at the edge crossings are 90 • . ...
arXiv:1808.10470v1
fatcat:vmoqfxp2ubbv3gd5fhv6nomura
Drawing graphs with right angle crossings
2011
Theoretical Computer Science
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This paper initiates the study of combinatorial and algorithmic questions related to the problem of computing RAC drawings with few bends per edge. ...
Namely, we study the interplay between number of bends per edge and total number of edges in RAC drawings. ...
(c) If G admits a RAC drawing with at most one bend per edge then m = O(n 4 3 ). (d) If G admits a RAC drawing with at most two bends per edge then m = O(n 7 4 ). ...
doi:10.1016/j.tcs.2011.05.025
fatcat:aapalbfrorfmvcdiacvhm4ss64
1-Bend RAC Drawings of 1-Planar Graphs
[article]
2016
arXiv
pre-print
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One of the main questions still open is whether every 1-planar graph has a RAC drawing with at most one bend per edge. We positively answer this question. ...
Also, straight-line RAC drawings always exist for IC-planar graphs, a subclass of 1-planar graphs. ...
Let G be an n-vertex 1-planar graph. Then G admits a 1-planar RAC drawing Γ with at most one bend per edge. ...
arXiv:1608.08418v1
fatcat:rzcne3zy2zbk3kbscfapxjdew4
Drawing Graphs with Right Angle Crossings
[chapter]
2009
Lecture Notes in Computer Science
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This paper initiates the study of combinatorial and algorithmic questions related with the problem of computing RAC drawings with few bends per edge. ...
Namely, we study the interplay between number of bends per edge and total number of edges in RAC drawings. ...
Drawing Graphs with Right Angle Crossings ...
doi:10.1007/978-3-642-03367-4_19
fatcat:jlucpnj6knf5nmjdrq6rryf3wi
A Survey on Graph Drawing Beyond Planarity
[article]
2018
arXiv
pre-print
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Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. ...
Aim of this survey is to describe the main research directions in this area, the most prominent known results, and some of the most challenging open problems. ...
Figure 6 (c) shows a 1-planar RAC drawing with at most one bend per edge of the graph in Fig. 6(b) . ...
arXiv:1804.07257v1
fatcat:xeckxilhfbbgdbfhctikymlq6m
RAC Drawings in Subcubic Area
[article]
2020
arXiv
pre-print
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., on the area of RAC drawings. ...
Given a graph with n vertices and m edges, we provide a RAC drawing algorithm with curve complexity 6 and area O(n^2.75), which takes time O(n+m). ...
in [11] ; there exists no RAC drawing of K n with 3 bends per edge in O(n 2 ) area for sufficiently large n; every graph admits a RAC drawing with 8 bends per edge in O(n 2 ) area. ...
arXiv:2001.02867v1
fatcat:7bwr5cqegbdmjjfjomyucj3bpy
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[chapter]
2012
Lecture Notes in Computer Science
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We investigate two drawing styles where only bends or both bends and edges must be drawn on an underlying grid. We present various results for drawings with one, two, and three bends per edge. ...
Part of this research has been presented as a poster at the 19th Int. Symposium on Graph Drawing, Eindhoven, 2011. ...
If such a drawing exists and the largest number of bends per edge in the drawing is b, we say that G admits a RAC b (or an αAC b ) embedding on S. ...
doi:10.1007/978-3-642-28076-4_19
fatcat:bfn6x7zlwna5tdbfhtomkuvr74
Graphs that admit right angle crossing drawings
2012
Computational geometry
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We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends per edge, then the number of edges is at most 6.5n and 74.2n, respectively. ...
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. ...
Acknowledgement We would like to acknowledge an anonymous referee for pointing out that K 6 has a RAC 1 drawing. ...
doi:10.1016/j.comgeo.2011.11.008
fatcat:6fbspb7qcja2dpdokkoqhtlewe
Graphs that Admit Right Angle Crossing Drawings
[chapter]
2010
Lecture Notes in Computer Science
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We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends per edge, then the number of edges is at most 6.5n and 74.2n, respectively. ...
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. ...
The size of a face is the number of edges (counted with multiplicity) on the boundary of f .
RAC Drawings with One Bend per Edge Discharging. ...
doi:10.1007/978-3-642-16926-7_14
fatcat:xpkrxoks6renjfqyja4dhziwsq
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[article]
2011
arXiv
pre-print
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We investigate two drawing styles where only bends or both bends and edges must be drawn on an underlying grid. We present various results for drawings with one, two, and three bends per edge. ...
Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. ...
If such a drawing exists and the largest number of bends per edge in the drawing is b, we say that G admits a RAC b (or an αAC b ) embedding on S. ...
arXiv:1107.4970v1
fatcat:i5ycjqcbojddtjvsgfunw45z4u
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[chapter]
2012
Lecture Notes in Computer Science
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Recent experiments on the readability of drawings [4] showed that polyline drawings with angles at edge crossings close to 90 • and a small number of bends per edge are just as readable as planar drawings ...
If such a drawing exists and the largest number of bends per edge in the drawing is b, we say that G admits a RAC b (or an αAC b ) embedding on S. ...
doi:10.1007/978-3-642-25878-7_43
fatcat:w3mzoh6oprfhxfzbus4wrmiy34
On Compact RAC Drawings
2020
European Symposium on Algorithms
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[Emilio Di Giacomo et al., 2011] by showing how to compute a RAC drawing with three bends per edge in cubic area. ...
As a counterpart, we prove that in general quadratic area is not sufficient for RAC drawings with three bends per edge. ...
Let Γ be a RAC drawing of K n with O(1) bends per edge. ...
doi:10.4230/lipics.esa.2020.53
dblp:conf/esa/Forster020
fatcat:r2vjw25zkfcoxi7t7wnwnnayje
On the Perspectives Opened by Right Angle Crossing Drawings
[chapter]
2010
Lecture Notes in Computer Science
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Second, we study if RAC drawings allow us to draw bounded-degree graphs with lower curve complexity than the one required by more constrained drawing conventions. ...
RAC drawings have been introduced because cognitive experiments provided evidence that increasing the number of crossings does not decrease the readability of the drawing if the edges cross at right angles ...
Further, every graph admits a RAC drawing with at most three bends per edge, and this curve complexity is required in infinitely many cases. ...
doi:10.1007/978-3-642-11805-0_5
fatcat:sdkmwoxbkjgm7kcm2sxqlvntuq
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
[article]
2018
arXiv
pre-print
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First, we show that every n-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size O(n) × O(n). ...
Then, we show that every n-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size O(n^3) × O(n^3). ...
Does any 1-planar graph admit a RAC poly 1 drawing? Can we draw any graph in RAC 0 with only right-angle crossings in polynomial area when we allow one or two bends per edge? ...
arXiv:1806.10044v4
fatcat:k2ysur7abfevdnkplhpxziguga
On the Perspectives Opened by Right Angle Crossing Drawings
2011
Journal of Graph Algorithms and Applications
Preserved Fulltext
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Second, we study if RAC drawings allow us to draw bounded-degree graphs with lower curve complexity than the one required by more constrained drawing conventions. ...
RAC drawings have been introduced because cognitive experiments provided evidence that increasing the number of crossings does not decrease the readability of the drawing if the edges cross at right angles ...
Further, every graph admits a RAC drawing with at most three bends per edge, and this curve complexity is required in infinitely many cases. ...
doi:10.7155/jgaa.00217
fatcat:hhlcmlbxdfhl7fj2t5i3d4d3he
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