Really straight graph drawings

Authors:
Vida Dujmović;Matthew Suderman;David R. Wood
Affiliations:
School of Computer Science, McGill University, Montréal, Canada;School of Computer Science, McGill University, Montréal, Canada;School of Computer Science, Carleton University, Ottawa, Canada
Venue:
GD'04 Proceedings of the 12th international conference on Graph Drawing
Year:
2004

Citing 7
Cited 9

Few slopes without colinearity

Discrete Mathematics
Graphs with E edges have pagenumber E O

Journal of Algorithms
Some results on tree decomposition of graphs

Journal of Graph Theory
A partial k-arboretum of graphs with bounded treewidth

Theoretical Computer Science
On the Computational Complexity of Upward and Rectilinear Planarity Testing

SIAM Journal on Computing
Rectangular drawings of planar graphs

Journal of Algorithms
The geometric thickness of low degree graphs

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry

Graph drawings with few slopes

Computational Geometry: Theory and Applications
Drawing cubic graphs with at most five slopes

Computational Geometry: Theory and Applications
Tree Drawings on the Hexagonal Grid

Graph Drawing
Geometric representation of cubic graphs with four directions

Computational Geometry: Theory and Applications
Drawing cubic graphs with at most five slopes

GD'06 Proceedings of the 14th international conference on Graph drawing
Minimum-segment convex drawings of 3-connected cubic plane graphs

COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Leftist canonical ordering

GD'09 Proceedings of the 17th international conference on Graph Drawing
The planar slope number of planar partial 3-trees of bounded degree

GD'09 Proceedings of the 17th international conference on Graph Drawing
Drawing cubic graphs with the four basic slopes

GD'11 Proceedings of the 19th international conference on Graph Drawing

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Abstract

We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with $\mathcal{O}({\rm log} n)$ slopes.