Mathematical Programming

, Volume 55, Issue 1–3, pp 129–168 | Cite as

Structural properties and decomposition of linear balanced matrices

  • Michele Conforti
  • M. R. Rao


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 words

Polyhedral combinatorics integrality of polytopes decomposition 


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Copyright information

© The Mathematical Programming Society, Inc. 1992

Authors and Affiliations

  • Michele Conforti
    • 1
  • M. R. Rao
    • 2
  1. 1.Dipartimento di MatematicaUniversità di PadoraPadovaItaly
  2. 2.Graduate School of Business AdministrationNew York UniversityUSA

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