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Let C be a uniform clutter and let A be the incidence matrix of C. We denote the column vectors of A by v1,. .. , vq. Under certain conditions we prove that C is vertex critical. If C satisfies the max-flow min-cut property, we prove that A diagonalizes over Z to an identity matrix and that v1,. .. , vq form a Hilbert basis. We also prove that if C has a… (More)

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