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We study the capacitated vehicle routing problem in graphic metrics (graphic CVRP). Our main contribution is a new lower bound on the cost of an optimal solution. For graphic metrics, this lower bound is tight and significantly stronger than the well-known bound for general metrics. The proof of the new lower bound is simple and combinatorial. Using this lower bound, we analyze the approximation ratio of the classical iterated tour partitioning algorithm combined with the TSP algorithms for graphic metrics of Christofides 1976, of Mömke-Svensson JACM 2016, and of Sebő-Vygen Combinatorica 2014. In particular, we obtain a 1.95-approximation for the graphic CVRP.
Mömke et al. (Tue,) studied this question.