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 $\Delta -1$ edge slopes suffice for every outerplanar graph with maximum degree $\Delta \ge 4$. 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 $\Delta \ge 4$ there is an outerplanar graph with maximum degree $\Delta$ that requires at least $\Delta -1$ distinct edge slopes in an outerplanar straight-line drawing.

Major revision of the whole paper

References in corpus (4)

• Drawings of Planar Graphs with Few Slopes and Segments
• Graph Drawings with Few Slopes
• The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree
• Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness