Knauer, Kolja
Micek, Piotr
Walczak, Bartosz
Outerplanar graph drawings with few slopes
Computational Geometry-Theory And Applications
0925-7721
10.1016/j.comgeo.2014.01.003
47
5
614-624
11
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 Delta - 1 edge slopes suffice for every outerplanar graph with maximum degree Delta >= 4. This improves on 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 with maximum degree Delta that requires at least Delta - 1 distinct edge slopes in an outerplanar straight-line drawing. (C) 2014 Elsevier B.V. All rights reserved.
Outerplanar graph;
Striagh-line drawing;
Slope number;
Elsevier Science Bv
Amsterdam
2014