# Edge-Minimum Saturated k-Planar Drawings

@inproceedings{Chaplick2021EdgeMinimumSK, title={Edge-Minimum Saturated k-Planar Drawings}, author={Steven Chaplick and Jonathan Rollin and Torsten Ueckerdt}, booktitle={Graph Drawing}, year={2021} }

For a class $\mathcal{D}$ of drawings of loopless multigraphs in the plane, a drawing $D \in \mathcal{D}$ is saturated when the addition of any edge to $D$ results in $D' \notin \mathcal{D}$. This is analogous to saturated graphs in a graph class as introduced by Turan (1941) and Erdős, Hajnal, and Moon (1964). We focus on $k$-planar drawings, that is, graphs drawn in the plane where each edge is crossed at most $k$ times, and the classes $\mathcal{D}$ of all $k$-planar drawings obeying a…

## 2 Citations

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…

Saturated k-Plane Drawings with Few Edges

- MathematicsArXiv
- 2020

This paper studies saturated $k-plane drawings with few edges, in which no edge can be added without violating $k$-planarity, and presents constructions withFew edges for different values of $ k$ and $\ell$.

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