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We prove that infinitely presented graphical $Gr(7)$ small cancellationgroups are acylindrically hyperbolic. In particular, infinitely presentedclassical $C(7)$-groups and, hence, classical $C'(\frac{1}{6})$-groups areacylindrically hyperbolic. We also prove the analogous statements for thelarger class of graphical small cancellation presentations over free products.We construct infinitely presented classical $C'(\frac{1}{6})$-groups thatprovide new examples of divergence functions of groups.

Infinitely presented graphical small cancellation groups are acylindrically hyperbolic