Geodesic
1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 755-762.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/517
Classification : 20-XX, 00-XX
Keywords: Gromov hyperbolic, slim triangle, curve graph, arc graph, unicorn 
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     author = {Sebastian Hensel and Piotr Przytycki and Richard C.H. Webb},
     title = {1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs},
     journal = {Journal of the European Mathematical Society},
     pages = {755--762},
     publisher = {mathdoc},
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Sebastian Hensel; Piotr Przytycki; Richard C.H. Webb. 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 755-762. doi : 10.4171/jems/517. http://geodesic.mathdoc.fr/articles/10.4171/jems/517/

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