Characterization of totally unimodular matrices
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We exposed the proof or the sufficient condition of this theorem as well as the one of Statement 3 at the Seminary on Combinatorial Problems of the Faculté des Sciences de Paris in January 1962. A. Ghouila-Houri gave independently a characterization [3] which could have been deduced however from our results. R. Gomory gave us recently a new proof of the sufficient condition. His proof, combined with ours, allows us to prove a simpler characterization :
[1] N. Sheibani,et al. Paris , 1894, The Hospital.
[2] I. Heller. On linear systems with integral valued solutions. , 1957 .
[3] C. Berge. Théorie des graphes et ses applications , 1958 .
[4] W. T. Tutte. Matroids and graphs , 1959 .