Outerplanar graph drawings with few slopes ✩

Abstract : We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that ∆ − 1 edge slopes suffice for every outerplanar graph with maximum degree ∆ 4. This improves on the previous bound of O(∆ 5), which was shown for planar partial 3-trees, a superclass of outerplanar graphs. Our bound is tight: for every ∆ 4 there is an outerplanar graph with maximum degree ∆ that requires at least ∆ − 1 distinct edge slopes in an outerplanar straight-line drawing.
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Kolja Knauer, Piotr Micek, Bartosz Walczak. Outerplanar graph drawings with few slopes ✩. Computational Geometry: Theory and Applications Computational Geometry @ ScienceDirect, 2014. ⟨hal-01457974⟩

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