Abstract.
The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: October 10, 2000 Final version received: April 11, 2002
Rights and permissions
About this article
Cite this article
de Werra, D. Variations on the Theorem of Birkhoff – von Neumann and Extensions. Graphs and Combinatorics 19, 263–278 (2003). https://doi.org/10.1007/s00373-002-0496-6
Issue Date:
DOI: https://doi.org/10.1007/s00373-002-0496-6