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Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system frac(1, 2) A x ≥ 1, x ≥ 0 is box totally dual integral (box-TDI) if and only ifG is a series-parallel graph; a by-product of this characterization is a structural description of a box-TDI system on matroids. Our results strengthen two previous theorems obtained respectively by Cornuéjols, Fonlupt, and Naddef and by Mahjoub which assert that both polyhedra {x {divides} frac(1, 2) A x ≥ 1, x ≥ 0} and {x {divides} frac(1, 2) A x ≥ 1, 1 ≥ x ≥ 0} are integral if G is series-parallel. © 2008 Elsevier B.V. All rights reserved.

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Discrete Applied Mathematics

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