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The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M), Maximum { k: M has k circuits ,(repetition, allowed) such that each element e of M is used at most 2w(e) times by these circuits = Minimum { ∑x ∈ X w(x): X is a collection of elements (repetition allowed) of M such that every circuit in M meets X at least twice}. Our characterization contains a complete solution to a research problem on 2-edge-connected subgraph polyhedra posed by Cornuéjols, Fonlupt, and Naddef in 1985, which was independently solved by Vandenbussche and Nemhauser in Vandenbussche and Nemhauser (J. Comb. Optim. 9:357-379, 2005). © 2008 Springer-Verlag.

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Mathematical Programming

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