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- W3081569775 abstract "In this paper we study the area requirements of planar greedy drawings of triconnected planar graphs. Cao, Strelzoff, and Sun exhibited a family (mathcal H) of subdivisions of triconnected plane graphs and claimed that every planar greedy drawing of the graphs in (mathcal {H}) respecting the prescribed plane embedding requires exponential area. However, we show that every n-vertex graph in (mathcal H) actually has a planar greedy drawing respecting the prescribed plane embedding on an (O(n)times O(n)) grid. This reopens the question whether triconnected planar graphs admit planar greedy drawings on a polynomial-size grid. Further, we provide evidence for a positive answer to the above question by proving that every n-vertex Halin graph admits a planar greedy drawing on an (O(n)times O(n)) grid. Both such results are obtained by actually constructing drawings that are convex and angle-monotone. Finally, we consider (alpha )-Schnyder drawings, which are angle-monotone and hence greedy if (alpha le 30^circ ), and show that there exist planar triangulations for which every (alpha )-Schnyder drawing with a fixed (alpha <60^circ ) requires exponential area for any resolution rule." @default.
- W3081569775 created "2020-09-08" @default.
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- W3081569775 date "2020-01-01" @default.
- W3081569775 modified "2023-09-25" @default.
- W3081569775 title "On the Area Requirements of Planar Greedy Drawings of Triconnected Planar Graphs" @default.
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- W3081569775 doi "https://doi.org/10.1007/978-3-030-58150-3_35" @default.
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