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

@article{Pia2018OnMW,
  title={On matrices with the Edmonds-Johnson property arising from bidirected graphs},
  author={Alberto Del Pia and Antoine Musitelli and Giacomo Zambelli},
  journal={J. Comb. Theory, Ser. B},
  year={2018},
  volume={130},
  pages={49-91}
}
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 [6]. It also extends a well known theorem of Edmonds and Johnson [5]. 

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