Universal Slope Sets for Upward Planar Drawings
Graph Drawing and Network Visualization: 26th International Symposium, GD 2018, Barcelona, Spain, September 26-28, 2018, Proceedings(2022)
摘要
We study universal sets of slopes for computing upward planar drawings of planar st -graphs. We first consider a subfamily of planar st -graphs, called bitonic st -graphs. We prove that every set 𝒮 of slopes containing the horizontal slope is universal for 1-bend upward planar drawings of bitonic st -graphs with maximum vertex degree , i.e., every such digraph admits a 1-bend upward planar drawing whose edge segments use only slopes in 𝒮 . This result is worst-case optimal in terms of number of slopes, and, for a suitable choice of 𝒮 , it gives rise to drawings with worst-case optimal angular resolution. We then prove that every such set 𝒮 can be used to construct 2-bend upward planar drawings of n -vertex planar st -graphs with at most 4n-9 bends in total.
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关键词
Slope number,Universal slope sets,Upward planarity,Planar st-graphs
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