Properties of balanced and perfect matrices

In this paper the authors define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of the present results is that if a matrix A is perfect then they can construct a polynomial number of submatrices A1,...,An, of A such that A is balanced if and only if all the submatrices A1,...,An of A are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.