# Drawing Graphs as Spanners

@article{Aichholzer2020DrawingGA, title={Drawing Graphs as Spanners}, author={Oswin Aichholzer and Manuel Borrazzo and Prosenjit Bose and Jean Cardinal and Fabrizio Frati and Pat Morin and Birgit Vogtenhuber}, journal={ArXiv}, year={2020}, volume={abs/2002.05580} }

We study the problem of embedding graphs in the plane as good geometric spanners. That is, for a graph $G$, the goal is to construct a straight-line drawing $\Gamma$ of $G$ in the plane such that, for any two vertices $u$ and $v$ of $G$, the ratio between the minimum length of any path from $u$ to $v$ and the Euclidean distance between $u$ and $v$ is small. The maximum such ratio, over all pairs of vertices of $G$, is the spanning ratio of $\Gamma$.
First, we show that deciding whether a graph… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 52 REFERENCES

## Optimal Monotone Drawings of Trees

VIEW 1 EXCERPT

## On plane geometric spanners: A survey and open problems

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Construction and Local Routing for Angle-Monotone Graphs

VIEW 1 EXCERPT

## Euclidean Greedy Drawings of Trees

VIEW 2 EXCERPTS

## Recognition and Complexity of Point Visibility Graphs

VIEW 4 EXCERPTS

## On Planar Greedy Drawings of 3-Connected Planar Graphs

VIEW 1 EXCERPT

## Strongly Monotone Drawings of Planar Graphs

VIEW 1 EXCERPT

## Good spanning trees in graph drawing

VIEW 1 EXCERPT