• Corpus ID: 227306140

Saturated k-Plane Drawings with Few Edges

@article{Klute2020SaturatedKD,
  title={Saturated k-Plane Drawings with Few Edges},
  author={Fabian Klute and Irene Parada},
  journal={ArXiv},
  year={2020},
  volume={abs/2012.02281}
}
A drawing of a graph is $k$-plane if no edge is crossed more than $k$ times. In this paper we study saturated $k$-plane drawings with few edges. This are $k$-plane drawings in which no edge can be added without violating $k$-planarity. For every number of vertices $n>k+1$, we present a tight construction with $\frac{n-1}{k+1}$ edges for the case in which the edges can self-intersect. If we restrict the drawings to be $\ell$-simple we show that the number of edges in saturated $k$-plane drawings… 

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