Outerplanar Graph Drawings with Few Slopes

Computational Geometry (Impact Factor: 0.48). 05/2012; 47(5). DOI: 10.1016/j.comgeo.2014.01.003
Source: arXiv


We consider straight-line outerplanar drawings of outerplanar graphs in which
the segments representing edges are parallel to a small number of directions.
We prove that Delta-1 directions suffice for every outerplanar graph with
maximum degree Delta>=4. This improves the previous bound of O(Delta^5), which
was shown for planar partial 3-trees, a superclass of outerplanar graphs. The
bound is tight: for every Delta>=4 there is an outerplanar graph of maximum
degree Delta which requires at least Delta-1 distinct edge slopes for an
outerplanar straight-line drawing.

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Available from: Kolja Knauer, Jul 29, 2014
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