Uniform Hyperbolicity for Arc Graphs and Curve Graphs

@inproceedings{Hensel2013UniformHF,
title={Uniform Hyperbolicity for Arc Graphs and Curve Graphs},
author={Sebastian Hensel and Piotr Przytycki and Richard C. H. Webb},
year={2013}
}

We describe unicorn paths in the arc graph and show that they form 1–slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7–hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17–hyperbolic, including closed surfaces.