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A sufficient condition for a matrix to be totally unimodular

F. G. Commoner

Abstract

Abstract Two conditions for a matrix to be totally unimodular are obtained; one sufficient, one necessary and sufficient. Both conditions involve a directed bipartite graph obtained from a {1, −1, 0}‐valued matrix, and both are generalizations of the fact that directed graphs and 2‐colorable undirected graphs have totally unimodular incidence matrices.

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Available abstract

Key concepts: Unimodular matrix, Incidence matrix, Mathematics, Combinatorics, Bipartite graph, Matrix (chemical analysis), Directed graph, Discrete mathematics