1-Bend Upward Planar Drawings of SP-Digraphs
نویسندگان
چکیده
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 d 2 e distinct slopes if biconnected, and with d 2 e + 1 distinct slopes if connected.
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