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A generalization of Evans' Theorem: embedding partial tricycle systems

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

C. C. Lindner  and
C. A. Rodger
C. C. Lindner
Affiliation:
Department of Discrete and Statistical Sciences 120 Mathematics AnnexAuburn University Alabama36849-5307, USA
C. A. Rodger
Affiliation:
Department of Discrete and Statistical Sciences 120 Mathematics AnnexAuburn University Alabama36849-5307, USA
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Abstract

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In 1960, Trevor Evans gave a best possible embedding of a partial latin square of order n in a latin square of order t, for any t ≥ 2n. A latin square of order n is equivalent to a 3-cycle system of Kn, n, n, the complete tripartite graph. Here we consider a small embedding of partial 3k-cycle systems of Kn, n, n of a certain type which generalizes Evans' Theorem, and discuss how this relates to the embedding of patterned holes, another recent generalization of Evans' Theorem.

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 399 - 408
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Evans, T., ‘Embedding incomplete latin squares’, Amer. Math. Monthly 67 (1960), 958–961.Google Scholar
[2]Lindner, C. C. and Rodger, C. A., ‘Generalized embedding theorems for partial latin squares’, Bull. ICA 5 (1992), 81–99.Google Scholar
[3]Lindner, C. C. and Rodger, C. A., ‘A partial m = (2k + 1)-cycle system of order n can be embedded in an m-cycle system of order (2n + 1)m’, Discrete Math. 117 (1993), 151–159.Google Scholar