Structural properties and decomposition of linear balanced matrices
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Claude Berge defines a (0, 1) matrix A to be linear ifA does not contain a 2 × 2 submatrix of all ones.A(0, 1) matrixA is balanced ifA does not contain a square submatrix of odd order with two ones per row and column.
The contraction of a rowi of a matrix consists of the removal of rowi and all the columns that have a 1 in the entry corresponding to rowi.
In this paper we show that if a linear balanced matrixA does not belong to a subclass of totally unimodular matrices, thenA orAT contains a rowi such that the submatrix obtained by contracting rowi has a block-diagonal structure.
Key wordsPolyhedral combinatorics integrality of polytopes decomposition
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