Really Straight Graph Drawings [chapter]

Vida Dujmović, Matthew Suderman, David R. Wood
2005 Lecture Notes in Computer Science  
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
more » ... considered. For example, it is proved that graphs of bounded degree and bounded treewidth have drawings with O(log n) slopes.
doi:10.1007/978-3-540-31843-9_14 fatcat:fwradttc6ba7jip6ftrdahsdwq