Hensel-Przytycki-Webb proved that the curve graphs of all orientable surfaces are 17-hyperbolic. In this paper, we show that the curve graphs of nonorientable surfaces are 17-hyperbolic by applying Hensel-Przytycki-Webb’s argument. We also show that the arc graphs of non-orientable surfaces are 7-hyperbolic, and arccurve graphs of (non-)orientable surfaces are 9-hyperbolic.
"Uniform hyperbolicity for curve graphs of non-orientable surfaces." Hiroshima Math. J. 46 (3) 343 - 355, November 2016. https://doi.org/10.32917/hmj/1487991626