Date of Original Version
Journal of Combinatorial Theory, Series B Volume 77, Issue 2, November 1999, Pages 292-406
Abstract or Description
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.