Drawing outer-1-planar graphs revisited

09/15/2020

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by   Therese Biedl, et al.

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In a recent article (Auer et al, Algorithmica 2016) it was claimed that every outer-1-planar graph has a planar visibility representation of area O(nlog n). In this paper, we show that this is wrong: There are outer-1-planar graphs that require Ω(n^2) area in any planar drawing. Then wegive a construction (using crossings, but preserving a given outer-1-planar embedding) that results in an orthogonal box-drawing with O(n log n) area and at most two bends per edge.