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Monotone Drawings of Planar Graphs
[chapter]

2002
*
Lecture Notes in Computer Science
*

Let G be a

doi:10.1007/3-540-36136-7_57
fatcat:5iuh2z7kf5hsjk6hkrmtnlfkli
*graph*drawn in the plane so that its edges are represented by x-*monotone*curves, any pair*of*which cross an even number*of*times. ... We show that G can be redrawn in such a way that the x-coordinates*of*the vertices remain unchanged and the edges become non-crossing straight-line segments. ... For any x-*monotone*even*drawing**of*a connected*graph*, there is an equivalent x-*monotone**drawing*in which no two edges cross each other and the x-coordinates*of*the corresponding vertices are the same. ...##
###
Monotone drawings of planar graphs
[article]

2011
*
arXiv
*
pre-print

Let G be a

arXiv:1101.0967v1
fatcat:q72qup7mrzdcdoxoegsv6nd3am
*graph*drawn in the plane so that its edges are represented by x-*monotone*curves, any pair*of*which cross an even number*of*times. ... We show that G can be redrawn in such a way that the x-coordinates*of*the vertices remain unchanged and the edges become non-crossing straight-line segments. ... For any x-*monotone*even*drawing**of*a connected*graph*, there is an equivalent x-*monotone**drawing*in which no two edges cross each other and the x-coordinates*of*the corresponding vertices are the same. ...##
###
Monotone drawings of planar graphs

2004
*
Journal of Graph Theory
*

Let G be a

doi:10.1002/jgt.10168
fatcat:2hzsmn4us5h7hcc6x6dwzy6adu
*graph*drawn in the plane so that its edges are represented by x-*monotone*curves, any pair*of*which cross an even number*of*times. ... We show that G can be redrawn in such a way that the x-coordinates*of*the vertices remain unchanged and the edges become non-crossing straight-line segments. ... For any x-*monotone*even*drawing**of*a connected*graph*, there is an equivalent x-*monotone**drawing*in which no two edges cross each other and the x-coordinates*of*the corresponding vertices are the same. ...##
###
Monotone Drawings of k-Inner Planar Graphs
[article]

2018
*
arXiv
*
pre-print

An outerplanar

arXiv:1808.06892v2
fatcat:d2hkcmoaerecraznc77dkmrztq
*graph*is a 0-inner*planar**graph*. In this paper, we show how to construct a*monotone**drawing**of*a k-inner*planar**graph*on a 2(k+1)n × 2(k+1)n grid. ... In the special case*of*an outerplanar*graph*, we can produce a*planar**monotone**drawing*on a n × n grid, improving previously known results. ...*Monotone**drawing**of*k-inner*planar**graphs*1: procedure k-InnerPlanarMonotoneDrawing(G) 2: Input: An n-vertex*planar**graph*G and an embedding*of*G with k inner vertices. 3: Output: A*monotone**planar**drawing*...##
###
Monotone Grid Drawings of Planar Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-319-08016-1_10
fatcat:fmizli4dq5ghjly7a7kcntnb6q
*monotone**drawing**of*a*planar**graph*G is a*planar*straightline*drawing**of*G where a*monotone*path exists between every pair*of*vertices*of*G in some direction. ... A*monotone**drawing**of*a*planar**graph*is a*monotone*grid*drawing*if every vertex in the*drawing*is drawn on a grid point. ... We call a*monotone**drawing**of*a*planar**graph*a*monotone*grid*drawing*if every vertex is drawn on a grid point. ...##
###
Strongly Monotone Drawings of Planar Graphs
[article]

2016
*
arXiv
*
pre-print

We present algorithms to compute crossing-free strongly

arXiv:1601.01598v1
fatcat:3hl7sgjhtbfdxniaf7prt3a4wa
*monotone**drawings*for some classes*of**planar**graphs*; namely, 3-connected*planar**graphs*, outerplanar*graphs*, and 2-trees. ... The*drawings**of*3-connected*planar**graphs*are based on primal-dual circle packings. ... Every 3-connected*planar**graph*has a strongly*monotone**drawing*. Proof. We show that the straight-line*drawing*corresponding to a primal-dual circle packing*of*a*graph*G is already strongly*monotone*. ...##
###
Monotone Grid Drawings of Planar Graphs
[article]

2013
*
arXiv
*
pre-print

A

arXiv:1310.6084v1
fatcat:vax3ekavn5dvznmsrxo6a365xy
*monotone**drawing**of*a*planar**graph*G is a*planar*straight-line*drawing**of*G where a*monotone*path exists between every pair*of*vertices*of*G in some direction. ... A*monotone**drawing**of*a*planar**graph*is a*monotone*grid*drawing*if every vertex in the*drawing*is drawn on a grid point. ... We call a*monotone**drawing**of*a*planar**graph*a*monotone*grid*drawing*if every vertex is drawn on a grid point. ...##
###
Strongly Monotone Drawings of Planar Graphs

2016
*
International Symposium on Computational Geometry
*

We present algorithms to compute crossing-free strongly

doi:10.4230/lipics.socg.2016.37
dblp:conf/compgeom/FelsnerIKKMS16
fatcat:2fa3uyreofa4lniu5oaie2warm
*monotone**drawings*for some classes*of**planar**graphs*; namely, 3-connected*planar**graphs*, outerplanar*graphs*, and 2-trees. ... The*drawings**of*3-connected*planar**graphs*are based on primal-dual circle packings. ... 1 Every 3-connected*planar**graph*has a strongly*monotone**drawing*. ...##
###
Strongly Monotone Drawings of Planar Graphs *

unpublished

We present algorithms to compute crossing-free strongly

fatcat:46xipw6jwjabng4dkonx2ws4ei
*monotone**drawings*for some classes*of**planar**graphs*; namely, 3-connected*planar**graphs*, outerplanar*graphs*, and 2-trees. ... The*drawings**of*3-connected*planar**graphs*are based on primal-dual circle packings. ... Every 3-connected*planar**graph*has a strongly*monotone**drawing*. Proof. We show that the straight-line*drawing*corresponding to a primal-dual circle packing*of*a*graph*G is already strongly*monotone*. ...##
###
Height-Preserving Transformations of Planar Graph Drawings
[chapter]

2014
*
Lecture Notes in Computer Science
*

There are numerous styles

doi:10.1007/978-3-662-45803-7_32
fatcat:i35d2e6i4batdkcmgp7aai2bm4
*of**planar**graph**drawings*, such as straight-line*drawings*, poly-line*drawings*, orthogonal*graph**drawings*and visibility representations. ... Given a*planar**drawing*in one*of*these styles, can it be converted it to another style while keeping the height unchanged? ... The*graph*in Fig. 3 has a*planar*poly-line*drawing*on 6 rows, but no*planar*y-*monotone*orthogonal*drawing*on 6 rows. Proof. ...##
###
Monotone Drawings of Graphs with Fixed Embedding
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we investigate

doi:10.1007/978-3-642-25878-7_36
fatcat:d6ofhrdr6bex5opoir45xg2nue
*planar**monotone**drawings*in the fixed embedding setting, i.e., a*planar*embedding*of*the*graph*is given as part*of*the input that must be preserved by the*drawing*algorithm ... A*drawing**of*a*graph*is a*monotone**drawing*if for every pair*of*vertices u and v, there is a path drawn from u to v that is*monotone*in some direction. ... this section we study*monotone**drawings**of*embedded*planar**graphs*. ...##
###
Monotone Drawings of Graphs with Fixed Embedding

2013
*
Algorithmica
*

In this paper we investigate

doi:10.1007/s00453-013-9790-3
fatcat:lbb3ofk56ncy3ct6kclavn4e74
*planar**monotone**drawings*in the fixed embedding setting, i.e., a*planar*embedding*of*the*graph*is given as part*of*the input that must be preserved by the*drawing*algorithm ... A*drawing**of*a*graph*is a*monotone**drawing*if for every pair*of*vertices u and v, there is a path drawn from u to v that is*monotone*in some direction. ... this section we study*monotone**drawings**of*embedded*planar**graphs*. ...##
###
On the number of upward planar orientations of maximal planar graphs

2014
*
Theoretical Computer Science
*

We consider the problem

doi:10.1016/j.tcs.2014.04.024
fatcat:gkwwxhkj4vgllne4uukg7u4vxy
*of*determining the maximum and the minimum number*of*upward*planar*orientations a maximal*planar**graph*can have. ... Moreover, there exist n-vertex maximal*planar**graphs*having as few as O(n · 2 n ) upward*planar*orientations and n-vertex maximal*planar**graphs*having Ω(2.599 n ) upward*planar*orientations. ... upward*planar**drawings**of*directed*graphs*(see, e.g., [1, 6] ). ...##
###
On the Number of Upward Planar Orientations of Maximal Planar Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

We consider the problem

doi:10.1007/978-3-642-35261-4_44
fatcat:yxunzi5uizbnhehk7sktc7mhy4
*of*determining the maximum and the minimum number*of*upward*planar*orientations a maximal*planar**graph*can have. ... Moreover, there exist n-vertex maximal*planar**graphs*having as few as O(n · 2 n ) upward*planar*orientations and n-vertex maximal*planar**graphs*having Ω(2.599 n ) upward*planar*orientations. ... upward*planar**drawings**of*directed*graphs*(see, e.g., [1, 6] ). ...##
###
Straightening out planar poly-line drawings
[article]

2014
*
arXiv
*
pre-print

Likewise y-

arXiv:1404.5892v2
fatcat:aumv4cy43zbjbbjwimhqf2dali
*monotonicity*is required: there are poly-line*drawings*(not y-*monotone*) that cannot be straightened out while maintaining the height. We give some applications*of*our result. ... We show that any y-*monotone*poly-line*drawing*can be straightened out while maintaining y-coordinates and height. ... Let Γ be a*planar*y-*monotone*poly-line*drawing**of*a triangulated*graph*G. ...
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