The associated graded algebras of Brauer graph algebras II: Infinite representation type

Let G be a Brauer graph and A the associated Brauer graph algebra. Denote by $\mathrm{gr}\left(A\right)$ the graded algebra associated with the radical filtration of A. The question when $\mathrm{gr}\left(A\right)$ is of finite representation type was answered in a previous paper. In the present paper, we characterize when $\mathrm{gr}\left(A\right)$ is domestic in terms of the associated Brauer graph G.