The Planar Slope Number of Planar Partial 3Trees of Bounded DegreeJelínek, Vít and Jelínková, Eva and Kratochvíl, Jan and Tesar, Marek and Vyskocil, Tomás (2010) The Planar Slope Number of Planar Partial 3Trees of Bounded Degree. In: Graph Drawing 17th International Symposium, GD 2009, September 2225, 2009 , pp. 304315(Official URL: http://dx.doi.org/10.1007/9783642118050_29). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783642118050_29
AbstractIt is known that every planar graph has a planar embedding where edges are represented by noncrossing straightline segments. We study the planar slope number, i.e., the minimum number of distinct edgeslopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every seriesparallel graph of maximum degree three is three. We also show that the planar slope number of every planar partial 3tree and also every plane partial 3tree is c at most 2O(Δ) . In particular, we answer the question of Dujmovi´ 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. Keywords: graph drawing; planar graphs; slopes; planar slope number.
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