Abstract. It is proved that every series-parallel digraph whose maximum vertex-degree is ∆ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of ∆ distinct slopes. This is shown to be worst-case optimal in terms of the number of slopes. Furthermore, our construction gives rise to drawings with optimal angular resolution π ∆ . A variant of the proof technique is used to show that (non-directed) reduced series-parallel graphs and flat series-parallel graphs have a (non-upward) one-bend planar drawing with
Concerning 1-bend drawings, Di Giacomo et al. REF proved that every series-parallel directed graph has an upward drawing with one bend per edge and Δ slopes.
1-bend Upward Planar Drawings of SP-digraphs
ArXiv
ArXiv
Mathematics Computer Science