A group is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group has a generating set such that the corresponding Cayley graph is a (non-elementary) quasi-tree and the action of on is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As an application, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.
"Acylindrical group actions on quasi-trees." Algebr. Geom. Topol. 17 (4) 2145 - 2176, 2017. https://doi.org/10.2140/agt.2017.17.2145