Decomposition of Balanced Matrices
journal contributionposted on 01.01.1986 by Michele Conforti, Gerard Cornuejols, M. R. Rao
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A 0, 1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0, 1 matrix is either totally unimodular or its bipartite representation has a cutset consisting of two adjacent nodes and some of their neighbors. This result yields a polytime recognition algorithm for balancedness. To prove the result, we first prove a decomposition theorem for balanced 0, 1 matrices that are not strongly balanced.