Drawing outer-1-planar graphs revisited
Copyright policy )Drawing outer-1-planar graphs revisited
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 $O(n\log n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs that require $\Omega(n^2)$ area in any planar drawing. Then we give 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.
- University of Waterloo Canada
- University of Waterloo (Canada) Canada
Computational Geometry (cs.CG), FOS: Computer and information sciences, Graph algorithms (graph-theoretic aspects), Computer Science - Computational Geometry, Planar graphs; geometric and topological aspects of graph theory
Computational Geometry (cs.CG), FOS: Computer and information sciences, Graph algorithms (graph-theoretic aspects), Computer Science - Computational Geometry, Planar graphs; geometric and topological aspects of graph theory
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