Drawings of planar graphs with few slopes and segments

We study straight-line drawings of planar 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 5 2 n segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). In a companion paper, drawings of non-planar graphs with few slopes are also considered. © 2006 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: COMGEO
• Authors: Vida Dujmovic, David Eppstein, Matthew Suderman, David R. Wood
• Keywords: 3-connected Plane Graph, Applied Computing, COMGEO 2007, Planar Graphs, Straight-line Drawings