Feasibility of the Mixed Postman Problem with Restrictions on the Edges

The mixed postman problem consists of finding a minimum cost tour of a connected mixed graph traversing all its vertices, edges, and arcs at least once. We consider the variant of the mixed postman problem where all edges must be traversed exactly once. The feasibility version of this problem is NP-complete. We introduce an infinite class of necessary conditions for feasibility, which we conjecture are also sufficient. We prove that no finite subset of these conditions is sufficient.