$1$-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 $v$....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1920-180X |