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.
@article{arxiv.math/0606450,
title = {Drawings of Planar Graphs with Few Slopes and Segments},
author = {Vida Dujmovic' and David Eppstein and Matthew Suderman and David R. Wood},
journal= {arXiv preprint arXiv:math/0606450},
year = {2008}
}
Comments
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