In this paper, we propose graph-based models for several vehicle routing problems with intermediate stops: the capacitated multi-trip vehicle routing problem with time windows, the multi-depot vehicle routing problem with inter-depot routes, the arc routing problem with intermediate facilities under capacity and length restrictions and the green vehicle routing problem. In these models, the set of feasible routes is represented by a set of resource constrained paths in one or several graphs. Intermediate stops are supported by the possibility to define negative resource consumption for some arcs. The models that we propose are then solved by VRPSolver, which implements a generic branch-cut-and-price exact algorithm. Thus, a simple parameterization enables us to use several state-of-the-art algorithmic components: automatic stabilization by dual price smoothing, limited-memory rank-1 cuts, reduced cost-based arc elimination, enumeration of elementary routes, and hierarchical strong branching. For each problem, we numerically compare the proposed methodology with the best exact approach found in the literature. State-of-the-art computational results were obtained for all problems except one.