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Comments on a Paper of R. A. Brualdi

Published online by Cambridge University Press:  20 November 2018

G. Bongiovanni ,
D. P. Bovet  and
A. Cerioli
G. Bongiovanni
Affiliation:
Dlpartimento di Matematica, Universita' Degli Studi di Roma "La Sapienza" Plazzale Aldo Moro 5 1-00185, Roma - Italy
D. P. Bovet
Affiliation:
Dlpartimento di Matematica, Universita' Degli Studi di Roma "La Sapienza" Plazzale Aldo Moro 5 1-00185, Roma - Italy
A. Cerioli
Affiliation:
Dlpartimento di Matematica, Universita' Degli Studi di Roma "La Sapienza" Plazzale Aldo Moro 5 1-00185, Roma - Italy
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Abstract

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R. A. Brualdi [1] presents a construction yielding matrices whose Birkhoff representation consists of the maximum number of permutation matrices and having 0(2n2 ) line sum. In this note a counterexample to such a construction is given. Furthermore, a new construction is presented, yielding matrices with lower line sums.

Keywords

15A5105C5052A25

Information

Type
Article Commentary
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 394 - 398
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Brualdi, R. A., Notes on the Birkhoff algorithm for doubly stochastic matrices Canad. Math. Bull., Vol 25 (2) (1982), pp. 191–199.Google Scholar
2. Brualdi, R. A., The diagonal hipergraph of a matrix ﹛bipartite graph) Discrete Math., Vol 27 (1979), pp. 127–147.Google Scholar