Really Straight Graph Drawings

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 O(log n) slopes.

• Type: Conference
• Year: 2004
• Where: GD
• Authors: Vida Dujmovic, Matthew Suderman, David R. Wood
• Keywords: 3-connected Plane Graph, Cubic 3-connected Plane, GD 2004, Straight-line Drawings