Balanced matrices

A 0,±10,±1 matrix is balanced   if, in every submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of 4. This definition was introduced by Truemper and generalizes the notion of balanced 0,10,1 matrix introduced by Berge. In this tutorial, we survey what is currently known about these matrices: polyhedral results, combinatorial and structural theorems, and recognition algorithms.