It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every series-parallel graph of maximum degree three is three. We also show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most 2O(Δ). In particular, we answer the question of Dujmović et al. [Computational Geometry 38 (3), pp. 194-212 (2007)] whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes. © 2010 Springer-Verlag.
CITATION STYLE
Jelínek, V., Jelínková, E., Kratochvíl, J., Lidický, B., Tesař, M., & Vyskočil, T. (2010). The planar slope number of planar partial 3-trees of bounded degree. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5849 LNCS, pp. 304–315). https://doi.org/10.1007/978-3-642-11805-0_29
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