In this paper we study the computational complexity of the vehicle routing problem (VRP) and of the split delivery vehicle routing problem (SDVRP) on some special classes of instances, characterized by special structures of the underlying graph, namely a line, a star, a tree and a circle. We both study the problems in the case of unlimited fleet (UF) and under the constraint that a limited fleet is available (LF).
ARCHETTI, C., FEILLET, D., GENDREAU, M. et SPERANZA, M.G. (2011). Complexity of the VRP and SDVRP. Transportation Research Part C: Emerging Technologies, 19(5), pp. 741-750.