On Auslander-Reiten components of algebras without external short paths
  We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete description of self-injective artin algebras whose Auslander-Reiten quiver admits a regular acyclic component without external short paths. 
Alicja Jaworska, Piotr Malicki, Andrzej Skowro\'nski
math.RT