J Austral Math Soc Ser A 59 pp399--408, 1995.

A Generalization of Evans' Theorem: Embedding Partial Tricycle Systems

C. C. Lindner and C. A. Rodger

Abstract

In 1960, Trevor Evans gave a best possible embedding of a partial latin square of order n in a latin square of orfer t, for any t ³ 2n. A latin square of order n is equivalent to a 3-cycle system of K_n,n,n, the complete tripartite graph. Here we consider a small embedding of partial 3k-cycle systems of K_n,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.

1991 AMS Subject Classification: 05B15

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Authors

C. C. Lindner

C. A. Rodger

Department of Discrete and Statistical Sciences, 120 Mathematics Annex, Auburn University, Alabama 36849-5307, USA.