Vida Dujmovic', David Eppstein, Matthew Suderman, David R. Wood
Published 2006-06-19Version 1
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.
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
Journal: Computational Geometry: Theory and Applications 38:194-212, 2007
Vertex coloring of plane graphs with nonrepetitive boundary paths
Edge Partitions of Optimal $2$-plane and $3$-plane Graphs
3-facial edge-coloring of plane graphs
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