Tight integral duality gap in the Chinese Postman problem

Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the minimum weight T-join and the maximum weighted integral packing of T-cut~. This difference is called the (Tjoin) integral duality gap. Let nF be the number of components in the optimal T-join, Ttl) = minimum weight T-join and IItI) = max weight integral packing of T-cuts then we have T., II., < nF 1. This result unifies and generalizes Fulkerson's result for ITI = 2 and Seymour's result