Outerplanar graph drawings with few slopes
ABSTRACT 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.