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The Hadamard conjecture and circuits of length four in a complete bipartite graph

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Charles H. C. Little  and
David J. Thuente
Charles H. C. Little
Affiliation:
Department of Mathematics, Royal Melbourne Institute of Technology Ltd., Melbourne, Victoria 3000, Australia
David J. Thuente
Affiliation:
Department of Mathematics, Purdue University at Fort Wayne, Indiana 46805, U.S.A.
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Abstract

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We show that the problem of settling the existence of an n × n Hadamard matrix, where n is divisible by 4, is equivalent to that of finding the cardinality of a smallest set T of 4-circuits in the complete bipartite graph K n, n, such that T contains at least one circuit of each copy of K2,3 in Kn, n.

MSC classification

Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 2 , August 1981 , pp. 252 - 256
Copyright
Copyright © Australian Mathematical Society 1982

References

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Wallis, J. S. (1972), Hadamard matrices, Lecture Notes in Mathematics 292, 273–489 (Springer-Verlag, New York).Google Scholar