On matrices with the Edmonds–Johnson property arising from bidirected graphs

In this paper we study totally half-modular matrices obtained from {0,±1}-matrices with at most two nonzero entries per column by multiplying by 2 some of the columns. We give an excluded-minor characterization of the matrices in this class having strong Chvàtal rank 1. Our result is a special case...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series B 2018-05, Vol.130, p.49-91
Main Authors: Del Pia, Alberto, Musitelli, Antoine, Zambelli, Giacomo
Format: Article
Language:English
Subjects:
Bidirected graphs
Combinatorial optimization
Edmonds–Johnson property
Excluded minors
Integer programming
Strong Chvátal rank
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Summary:In this paper we study totally half-modular matrices obtained from {0,±1}-matrices with at most two nonzero entries per column by multiplying by 2 some of the columns. We give an excluded-minor characterization of the matrices in this class having strong Chvàtal rank 1. Our result is a special case of a conjecture by Gerards and Schrijver [11]. It also extends a well known theorem of Edmonds and Johnson [10].
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2017.09.013