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

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1982

References

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