Abstract. In the Mixed Chinese Postman Problem (MCPP), given an edge-weighted mixed graph G (G may have both edges and arcs), our aim is to find a minimum weight closed walk traversing each edge and arc at least once. The MCPP parameterized by the number of edges was known to be fixed-parameter tractable using a simple argument. Solving an open question of van Bevern et al., we prove that the MCPP parameterized by the number of arcs is also fixed-parameter tractable. Our proof is more involved and, in particular, uses a very useful result of Marx, O'Sullivan and Razgon (2013) on the treewidth of torso graphs with respect to small separators.

It is well-known that the Chinese Postman Problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese Postman Problem on mixed graphs, i.e., graphs with directed and undirected edges, for which the problem is NP-hard.

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