• Corpus ID: 227306140

# Saturated k-Plane Drawings with Few Edges

@article{Klute2020SaturatedKD,
title={Saturated k-Plane Drawings with Few Edges},
journal={ArXiv},
year={2020},
volume={abs/2012.02281}
}
• Published 3 December 2020
• Mathematics
• ArXiv
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…
1 Citations

## Figures and Tables from this paper

• 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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