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Journal Article

Odd Minimum Cut-Sets and b-Matchings

Manfred W. Padberg and M. R. Rao
Mathematics of Operations Research
Vol. 7, No. 1 (Feb., 1982), pp. 67-80
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3689360
Page Count: 14
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Odd Minimum Cut-Sets and b-Matchings
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Abstract

We show that the determination of a minimum cut-set of odd cardinality in a graph with even and odd vertices can be dealt with by a minor modification of the polynomially bounded algorithm of Gomory and Hu for multi-terminal networks. We connect this problem to the problem of identifying a matching (or blossom) constraint that chops off a point which is not contained in the convex hull of matchings or proving that no such inequality exists. Both the b-matching problems without and with upper bounds are considered. We discuss how the results of this paper can be used in conjunction with commercial LP packages to solve b-matching problems.

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