Page "Unimodular matrix" Paragraph 31

5.

Ghouila-Houri showed that a matrix is TU iff for every subset R of rows, there is an assignment of signs to rows so that the signed sum ( which is a row vector of the same width as the matrix ) has all its entries in ( i. e. the row-submatrix has discrepancy at most one ).

This and several other if-and-only-if characterizations are proven in Schrijver ( 2003 ).