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.
|Number of pages||11|
|Journal||Lecture Notes in Computer Science|
|Publication status||Published - 1 Dec 2004|
|Event||12th International Symposium on Graph Drawing, GD 2004 - New York, United States of America|
Duration: 29 Sep 2004 → 2 Oct 2004