Abstract
The problem of finding a T-join of minimum cardinality is studied. This problem includes the Chinese Postman Problem, the Shortest Path Problem and the Maximum Matching Problem. It is also closely related to the plane multicommodity flows and to the Shortest Cycle Cover Problem and still is polynomially solvable (see, e.g., [1]). For any even subset T of the vertex set of a connected graph G the minimum possible size τ(G, T) of a T-join in G does not exceed the maximum number v/(G, T) of disjoint T-cuts in G. In case G is bipartite, we have the equality v(G, T) = τ(G, T) (see [2]). A. Frank, A. Sebö, and E. Tardos [3] have proved that one can choose a packing of τ(G, T) T-cuts satisfying some additional requirements. In the present paper, we show that these requirements may be stronger, which is used to obtain upper bounds on τ(G, T).
This research was partially supported by the Russian Foundation of Fundamental Research (Grant 93–01–01486) and the International Science Foundation (Grant RPY000).
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© 1996 Kluwer Academic Publishers
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Kostochka, A.V. (1996). A Refinement of the Frank-Sebő-Tardos Theorem and Its Applications. In: Korshunov, A.D. (eds) Discrete Analysis and Operations Research. Mathematics and Its Applications, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1606-7_9
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DOI: https://doi.org/10.1007/978-94-009-1606-7_9
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