# 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…

## One Citation

### Saturated $2$-planar drawings with few edges

- Mathematics
- 2021

A drawing of a graph is k-plane if every edge contains at most k crossings. A k-plane drawing is saturated if we cannot add any edge so that the drawing remains k-plane. It is well-known that…

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