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Area, Curve Complexity, and Crossing Resolution of Non-planar Graph Drawings
[chapter]

2010
*
Lecture Notes in Computer Science
*

In this paper we study

doi:10.1007/978-3-642-11805-0_4
fatcat:a56qxno5zfgffog2azbhy3m4ri
*non*-*planar**drawings**of**graphs*,*and*study tradeoffs between the*crossing**resolution*(i.e., the minimum angle formed by two*crossing*segments), the*curve**complexity*(i.e., maximum ... number*of*bends per edge), the total number*of*bends,*and*the*area*. ... It is worth mentioning that, if no requirement about the*crossing**resolution*exists, then every*planar**graph*admits a*non*-*planar**drawing*in O(n)*area*[9] . ...##
###
On the Perspectives Opened by Right Angle Crossing Drawings

2011
*
Journal of Graph Algorithms and Applications
*

Third, we consider a natural

doi:10.7155/jgaa.00217
fatcat:hhlcmlbxdfhl7fj2t5i3d4d3he
*non*-*planar*generalization*of**planar*embedded*graphs*. Here we give bounds for*curve**complexity**and**area*different from the ones known for*planar*embeddings. ... We prove that every*graph*with vertex-degree at most 6 (at most 3) admits a RAC*drawing*with*curve**complexity*2 (resp. 1)*and*with quadratic*area*. ... We show that such*graphs*always admit RAC*drawings*with*curve**complexity*1*and*that such a*curve**complexity*is sometimes required. ...##
###
On the Perspectives Opened by Right Angle Crossing Drawings
[chapter]

2010
*
Lecture Notes in Computer Science
*

Third, we consider a natural

doi:10.1007/978-3-642-11805-0_5
fatcat:sdkmwoxbkjgm7kcm2sxqlvntuq
*non*-*planar*generalization*of**planar*embedded*graphs*. Here we give bounds for*curve**complexity**and**area*different from the ones known for*planar*embeddings. ... We prove that every*graph*with vertex-degree at most 6 (at most 3) admits a RAC*drawing*with*curve**complexity*2 (resp. 1)*and*with quadratic*area*. ... We show that such*graphs*always admit RAC*drawings*with*curve**complexity*1*and*that such a*curve**complexity*is sometimes required. ...##
###
Semi-bipartite Graph Visualization for Gene Ontology Networks
[chapter]

2010
*
Lecture Notes in Computer Science
*

*Area*,

*Curve*

*Complexity*,

*and*

*Crossing*

*Resolution*

*of*

*Non*-

*Planar*

*Graph*

*Drawings*Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta,

*and*Henk Meijer Abstract: In this paper we study

*non*-

*planar*

*drawings*

*of*

*graphs*... Third, we consider a natural

*non*-

*planar*generalization

*of*

*planar*embedded

*graphs*. Here we give bounds for

*curve*-

*complexity*

*and*

*area*different from the ones known for

*planar*embeddings. ...

##
###
A Framework for Drawing Planar Graphs with Curves and Polylines
[chapter]

1998
*
Lecture Notes in Computer Science
*

We describe a unified framework

doi:10.1007/3-540-37623-2_12
fatcat:k2yepvnn6vdchl2gzdbb6ppkcu
*of*aesthetic criteria*and**complexity*measures for*drawing**planar**graphs*with polylines*and**curves*. ...*and*edge representational*complexity**and*the*area**of*the*drawing*. ... For example, it seems that a*drawing**of*a*planar**graph*produced by this algorithm may have edge*crossings*. ...##
###
A Framework for Drawing Planar Graphs with Curves and Polylines

2000
*
Journal of Algorithms
*

We describe a unified framework

doi:10.1006/jagm.2000.1115
fatcat:wbs2a25s5bbzvpbbkbgi7bodsa
*of*aesthetic criteria*and**complexity*measures for*drawing**planar**graphs*with polylines*and**curves*. ...*and*edge representational*complexity**and*the*area**of*the*drawing*. ... For example, it seems that a*drawing**of*a*planar**graph*produced by this algorithm may have edge*crossings*. ...##
###
Delta-confluent Drawings
[article]

2005
*
arXiv
*
pre-print

We generalize the tree-confluent

arXiv:cs/0510024v1
fatcat:z74wsvnuijglfhqac42jxbwd7i
*graphs*to a broader class*of**graphs*called Delta-confluent*graphs*. This class*of**graphs**and*distance-hereditary*graphs*, a well-known class*of**graphs*, coincide. ... Some results about the visualization*of*Delta-confluent*graphs*are also given. ... One way to visualize a*non*-*planar**graph*is to find a maximum*planar*subgraph*of*the original*graph*, compute a*planar**drawing**of*the subgraph,*and*add the rest*of*the original*graph*back on the*drawing*. ...##
###
Graph drawing
[chapter]

2004
*
Handbook of Discrete and Computational Geometry, Second Edition
*

Bounds on geometric

doi:10.1201/9781420035315.ch52
fatcat:suzr5ked2veg7pmtmgpfppvrua
*and*topological properties*of**drawings*(e.g.,*area**and**crossings*) are presented in Section 1.2. Section 1.3 deals with the time*complexity**of*fundamental*graph**drawing*problems. ... BOUNDS ON THE*AREA*bound on the angular*resolution**of**planar*straight-line*drawings**of**planar**graphs*. ...##
###
Smooth Orthogonal Layouts
[chapter]

2013
*
Lecture Notes in Computer Science
*

We study the problem

doi:10.1007/978-3-642-36763-2_14
fatcat:5zg4c4omgrekrmuocaklaaqxha
*of*creating smooth orthogonal layouts for*planar**graphs*. ... Using the Kandinsky model for removing the degree restriction, we show that any*planar**graph*has a smooth*complexity*-2 layout. The work*of*M.A. ... Nöllenburg*and*I. Rutter for helpful discussions. ...##
###
Smooth Orthogonal Layouts

2013
*
Journal of Graph Algorithms and Applications
*

We study the problem

doi:10.7155/jgaa.00305
fatcat:cpyhzz7ks5gqrim3xsxpu3nqpy
*of*creating smooth orthogonal layouts for*planar**graphs*. ... Using the Kandinsky model for removing the degree restriction, we show that any*planar**graph*has a smooth*complexity*-2 layout. The work*of*M.A. ... Nöllenburg*and*I. Rutter for helpful discussions. ...##
###
Delta-Confluent Drawings
[chapter]

2006
*
Lecture Notes in Computer Science
*

We generalize the tree-confluent

doi:10.1007/11618058_16
fatcat:jc6se5vncvcszdiej5pzswonom
*graphs*to a broader class*of**graphs*called ∆-confluent*graphs*. This class*of**graphs**and*distancehereditary*graphs*, a well-known class*of**graphs*, coincide. ... Some results about the visualization*of*∆-confluent*graphs*are also given. ... One way to visualize a*non*-*planar**graph*is to find a maximum*planar*subgraph*of*the original*graph*, compute a*planar**drawing**of*the subgraph,*and*add the rest*of*the original*graph*back on the*drawing*. ...##
###
Page 6089 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

*and*edge representational

*complexity*

*and*the

*area*

*of*the

*drawing*. ... Summary: “We describe a unified framework

*of*aesthetic criteria

*and*

*complexity*measures for

*drawing*

*planar*

*graphs*with poly- lines

*and*

*curves*. ...

##
###
Beyond-Planar Graphs: Algorithmics and Combinatorics (Dagstuhl Seminar 16452)

2017
*
Dagstuhl Reports
*

The seminar brought together 29 researchers in the

doi:10.4230/dagrep.6.11.35
dblp:journals/dagstuhl-reports/Hong0KP16
fatcat:gmft5jywxbapza52lhj4o23ngq
*areas**of**graph*theory, combinatorics, computational geometry,*and**graph**drawing*. ... The common interest was in the exploration*of*structural properties*and*the development*of*algorithms for so-called beyond-*planar**graphs*, i.e.,*non*-*planar**graphs*with topological constraints such as specific ... Is it true that every*graph**of*maximum degree ∆ = 3 (∆ = 4) admits a (*non*-geometric, that is, with*curves*) both quasi-*planar**and*fan-*crossing*-free*drawing*? ...##
###
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. ... On the other hand, if we insist in having a constant number

*of*

*crossings*per edge,

*planar*

*and*

*non*-

*planar*

*drawings*

*of*

*planar*

*graphs*have in general the same

*area*requirement. ...

##
###
Lombardi Drawings of Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

We describe algorithms for finding Lombardi

doi:10.1007/978-3-642-18469-7_18
fatcat:jdtbo3ytbfamrnjmltfjs4e5a4
*drawings**of*regular*graphs*,*graphs**of*bounded degeneracy,*and*certain families*of**planar**graphs*. ... We introduce the notion*of*Lombardi*graph**drawings*, named after the American abstract artist Mark Lombardi. ...*Non*-*Crossing*Lombardi*Drawings**Planar**Graphs*Without*Planar*Lombardi*Drawings*Not every*planar**graph*has a*planar*Lombardi*drawing*. ...
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