Drawings of planar graphs with few slopes and segments

Vida Dujmovic, David Eppstein, Matthew Suderman, David R. Wood

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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 52n 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.
Original languageEnglish
Pages (from-to)194-212
Number of pages19
JournalComputational Geometry: Theory and Applications
Issue number3
Publication statusPublished - 2007
Externally publishedYes

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