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Small embeddings of partial directed cycle systems

Published online by Cambridge University Press:  17 April 2009

C.C. Lindner  and
C.A. Rodger
C.C. Lindner
Affiliation:
Department of Algebra, Combinatorics and Analysis Auburn, University Auburn, AL 36849–5307, United States of America
C.A. Rodger
Affiliation:
Department of Algebra, Combinatorics and Analysis Auburn, University Auburn, AL 36849–5307, United States of America
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Abstract

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In this paper, a generalisation of the Andersen, Hilton, Rodger Theorem for embedding partial idempotent latin squares is proved. This result is then used to prove that a partial directed m-cycle system of order n can be embedded in a directed m-cycle system of order (2n + 1)m if m is odd, of order 2nm if m ≥ 8 is even, 12n + 1 if m = 6 and approximately 2n + √2n if m = 4.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 213 - 224
Copyright
Copyright © Australian Mathematical Society 1992

References

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