A Generalization of Tutteʹs Characterization of Totally Unimodular Matrices

We characterize the symmetric (0, 1)-matrices that can be signed symmetrically so that every principal submatrix has determinant 0, ±1. This characterization generalizes Tutteʹs famous characterization of totally unimodular matrices. The result can be viewed as an excluded minor theorem for an interesting class of delta-matroids.