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An Elementary Proof of Johnson–Dulmage–Mendelsohn's Refinement of Birkhoff's Theorem on Doubly Stochastic Matrices

Published online by Cambridge University Press:  20 November 2018

Akihiro Nishi
Akihiro Nishi*
Affiliation:
Dept. of Mathematics Faculty of Education Saga University, 840 Saga, Japan
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Summary

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A purely combinatorial and elementary proof of Johnson-Dulmage-Mendelsohn's theorem, which gives a quite sharp upper bound on the number of permutation matrices needed for representing a doubly stochastic matrix by their convex combination, is given.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 1 , 01 March 1979 , pp. 81 - 86
Copyright
Copyright © Canadian Mathematical Society 1979

References

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