Let k be an arbitrary field and Q be an acyclic quiver of tame type (that is, of type˜ An, ˜Dn, ˜E6, ˜E7, ˜E8). Consider the path algebra kQ, the category of finite-dimensional right modules mod-kQ, and the minimal positive imaginary root of Q, denoted by δ. In the first part of the paper, we deduce that the Gabriel–Roiter (GR) inclusions in preprojective indecomposables and homoge…