Abstract
We study the Chinese postman (CP) cooperative game induced by a connected, weighted, undirected graph G, wherein players reside at the edges of G and a postman, starting from a post-office location (i.e., a vertex of G), needs to traverse all edges before returning to the post-office. We provide a complete characterization of all connected graphs for which there exists a positive edge-cost function such that the induced CP game has a non-empty core, and, consequently, we derive a complete characterization of all connected graphs for which there does not exist a positive edge-cost function which induces a CP game with a non-empty core. Membership in these classes of graphs can be verified in strongly polynomial time.
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