Outerplanar graph drawings with few slopes ?
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 ? ? 1 edge slopes suffice for every outerplanar graph with maximum degree ??4 ? ? 4 . This improves on the previous bound of O(?5) O ( ? 5 ) , which was shown for planar partial 3-trees, a superclass of outerplanar graphs. The bound is tight: for every ??4 ? ? 4 there is an outerplanar graph with maximum degree ?  that requires at least ??1 ? ? 1 distinct edge slopes in an outerplanar straight-line drawing.
outerplanar graph striagh-line drawing slope number