2006/06/19 by Vida Dujmovic', David Eppstein, Matthew Suderman +1 · 1 citation
Mathematics · #math.CO
paper · pdf · doi:10.1016/j.comgeo.2006.09.002
published as Computational Geometry: Theory and Applications 38:194-212, 2007 · This paper is submitted to a journal. A preliminary version appeared as "Really Straight Graph Drawings" in the Graph Drawing 2004 conference. See http://arxiv.org/math/0606446 for a companion paper
arxiv created 2006/06/19 · arxiv updated 2009/12/01
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.