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.
Cite this article
Sebastian Hensel, Piotr Przytycki, Richard C.H. Webb, 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 755–762DOI 10.4171/JEMS/517