Drawings of Planar Graphs with Few Slopes and Segments
Vida Dujmovic', David Eppstein, Matthew Suderman, David R. Wood
Abstract
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 5/2n 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.
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