We study straight-line drawings of 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 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). Drawings of non-planar graphs with few slopes are also considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with script O sign(log n) slopes.

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Conference 12th International Symposium on Graph Drawing, GD 2004
Citation
Dujmović, V, Suderman, M. (Matthew), & Wood, D. (2004). Really straight graph drawings. Presented at the 12th International Symposium on Graph Drawing, GD 2004.