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arXiv · 1608.08425

1-bend Upward Planar Drawings of SP-digraphs

Emilio Di Giacomo·Giuseppe Liotta·Fabrizio Montecchiani
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Abstract

It is proved that every series-parallel digraph whose maximum vertex-degree is $\Delta$ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of $\Delta$ 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 $\frac{\pi}{\Delta}$. 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 $\lceil\frac{\Delta}{2}\rceil$ distinct slopes if biconnected, and with $\lceil\frac{\Delta}{2}\rceil+1$ distinct slopes if connected.

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Emilio Di Giacomo, Giuseppe Liotta, Fabrizio Montecchiani. 2016-08-30. 1-bend Upward Planar Drawings of SP-digraphs. https://arxiv.org/abs/1608.08425

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