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On RAC Drawings of Graphs with one Bend per Edge
[article]

2018
*
arXiv
*
pre-print

A k-

arXiv:1808.10470v1
fatcat:vmoqfxp2ubbv3gd5fhv6nomura
*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 • . ...##
###
Drawing graphs with right angle crossings

2011
*
Theoretical Computer Science
*

This paper initiates the study

doi:10.1016/j.tcs.2011.05.025
fatcat:aapalbfrorfmvcdiacvhm4ss64
*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 ). ...##
###
1-Bend RAC Drawings of 1-Planar Graphs
[article]

2016
*
arXiv
*
pre-print

*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*. ...

##
###
Drawing Graphs with Right Angle Crossings
[chapter]

2009
*
Lecture Notes in Computer Science
*

This paper initiates the study

doi:10.1007/978-3-642-03367-4_19
fatcat:jlucpnj6knf5nmjdrq6rryf3wi
*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 ...##
###
A Survey on Graph Drawing Beyond Planarity
[article]

2018
*
arXiv
*
pre-print

*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) . ...

##
###
RAC Drawings in Subcubic Area
[article]

2020
*
arXiv
*
pre-print

.,

arXiv:2001.02867v1
fatcat:7bwr5cqegbdmjjfjomyucj3bpy
*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. ...##
###
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[chapter]

2012
*
Lecture Notes in Computer Science
*

We investigate two

doi:10.1007/978-3-642-28076-4_19
fatcat:bfn6x7zlwna5tdbfhtomkuvr74
*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. ...##
###
Graphs that admit right angle crossing drawings

2012
*
Computational geometry
*

We show that if a

doi:10.1016/j.comgeo.2011.11.008
fatcat:6fbspb7qcja2dpdokkoqhtlewe
*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*. ...##
###
Graphs that Admit Right Angle Crossing Drawings
[chapter]

2010
*
Lecture Notes in Computer Science
*

We show that if a

doi:10.1007/978-3-642-16926-7_14
fatcat:xpkrxoks6renjfqyja4dhziwsq
*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. ...##
###
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[article]

2011
*
arXiv
*
pre-print

We investigate two

arXiv:1107.4970v1
fatcat:i5ycjqcbojddtjvsgfunw45z4u
*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. ...##
###
Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles
[chapter]

2012
*
Lecture Notes in Computer Science
*

Recent experiments

doi:10.1007/978-3-642-25878-7_43
fatcat:w3mzoh6oprfhxfzbus4wrmiy34
*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. ...##
###
On Compact RAC Drawings

2020
*
European Symposium on Algorithms
*

[Emilio Di Giacomo et al., 2011] by showing how to compute a

doi:10.4230/lipics.esa.2020.53
dblp:conf/esa/Forster020
fatcat:r2vjw25zkfcoxi7t7wnwnnayje
*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*. ...##
###
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
[article]

2018
*
arXiv
*
pre-print

First, we show that every n-vertex NIC-planar

arXiv:1806.10044v4
fatcat:k2ysur7abfevdnkplhpxziguga
*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*? ...##
###
On the Perspectives Opened by Right Angle Crossing Drawings
[chapter]

2010
*
Lecture Notes in Computer Science
*

Second, we study if

doi:10.1007/978-3-642-11805-0_5
fatcat:sdkmwoxbkjgm7kcm2sxqlvntuq
*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. ...##
###
On the Perspectives Opened by Right Angle Crossing Drawings

2011
*
Journal of Graph Algorithms and Applications
*

Second, we study if

doi:10.7155/jgaa.00217
fatcat:hhlcmlbxdfhl7fj2t5i3d4d3he
*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. ...
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