A 0,¸±1-matrix A is balanced if, in every submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This definition was introduced by Truemper and generalizes the notion of a balanced 0,1-matrix introudced by Berge. In this paper the authors extend a bicoloring theorem of Berge and total dual integrality results of Fulkerson, Hoffman and Oppenheim to balanced 0,¸±1-matrices.
