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Minimal Interchanges of (0, 1)-Matrices and Disjoint Circuits in a Graph

Published online by Cambridge University Press:  20 November 2018

David W. Walkup
David W. Walkup*
Affiliation:
Boeing Scientific Research Laboratories, Seattle, Washington
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In this paper we obtain a partial answer in graph-theoretic form to a question raised by Ryser (2, p. 68) concerning the minimal number of interchanges required to transform equivalent (0, l)-matrices into each other.

For given positive integers m and n we consider the collection of m × n (0, 1)-matricesA = {aij}, i.e. aij = 0 or 1 for 1 ≤ i ≤ m, 1 ≤ j ≤ n. We say the (0, 1)-matrices A = {aij} and B = {bij} are equivalent and write A ~ B if and only if they have the same row and column sums, that is, if and only if.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 831 - 838
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Ryser, H. J., Combinatorial properties of matrices of zeros and ones. Can. J. Math., 9 (1957), 371–377.Google Scholar
2. Ryser, H. J., Combinatorial mathematics, The Carus Mathematical Monographs no. 14 (Mathematical Association of America, 1963).Google Scholar