$1$-string $B_2$-VPG representation of planar graphs
In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation—a string representation using paths in a rectangular grid that contain at most two bends. Furthermore, two paths representing vertices $u,v$ intersect precisely once whenever there is an edge between $u$ and $v$....
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| Format: | Article |
| Language: | English |
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Carleton University
2016-09-01
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| Series: | Journal of Computational Geometry |
| Online Access: | http://jocg.org/index.php/jocg/article/view/296 |
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doaj-1184d4051bd4495ebbff520d254dd2242020-11-24T23:58:49ZengCarleton UniversityJournal of Computational Geometry1920-180X2016-09-017210.20382/jocg.v7i2a8104$1$-string $B_2$-VPG representation of planar graphsTherese Biedl0Martin Derka1University of WaterlooUniversity of WaterlooIn this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation—a string representation using paths in a rectangular grid that contain at most two bends. Furthermore, two paths representing vertices $u,v$ intersect precisely once whenever there is an edge between $u$ and $v$. We also show that only a subset of the possible curve shapes is necessary to represent $4$-connected planar graphs.http://jocg.org/index.php/jocg/article/view/296 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Therese Biedl Martin Derka |
| spellingShingle |
Therese Biedl Martin Derka $1$-string $B_2$-VPG representation of planar graphs Journal of Computational Geometry |
| author_facet |
Therese Biedl Martin Derka |
| author_sort |
Therese Biedl |
| title |
$1$-string $B_2$-VPG representation of planar graphs |
| title_short |
$1$-string $B_2$-VPG representation of planar graphs |
| title_full |
$1$-string $B_2$-VPG representation of planar graphs |
| title_fullStr |
$1$-string $B_2$-VPG representation of planar graphs |
| title_full_unstemmed |
$1$-string $B_2$-VPG representation of planar graphs |
| title_sort |
$1$-string $b_2$-vpg representation of planar graphs |
| publisher |
Carleton University |
| series |
Journal of Computational Geometry |
| issn |
1920-180X |
| publishDate |
2016-09-01 |
| description |
In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation—a string representation using paths in a rectangular grid that contain at most two bends. Furthermore, two paths representing vertices $u,v$ intersect precisely once whenever there is an edge between $u$ and $v$. We also show that only a subset of the possible curve shapes is necessary to represent $4$-connected planar graphs. |
| url |
http://jocg.org/index.php/jocg/article/view/296 |
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