Postman tour on a graph with precedence relation on arcs

Since the introduction of the Chinese Postman Problem (CPP), many variations on the same theme have been developed. In this paper we examine still another variation. The arcs of the graph are partitioned and a precedence relation defined, specifying the order in which the elements of the partition have to be traversed. We first examine the conditions for a feasible solution to the problem. Next, we specify the graph properties of the precedence partition that insure a polynomial complexity solution of O(N⁵), where N is the number of nodes in the original graph. When the precedence relation on sets of arcs is general, we prove that the problem of finding the minimum length of feasible postman tour is NP‐complete.