%0 Journal Article
%T Drawings of Planar Graphs with Few Slopes and Segments
%A Vida Dujmovic'
%A David Eppstein
%A Matthew Suderman
%A David R. Wood
%J Mathematics
%D 2006
%I arXiv
%R 10.1016/j.comgeo.2006.09.002
%X 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.
%U http://arxiv.org/abs/math/0606450v1