A GENERALIZATION OF EVANS THEOREM - EMBEDDING PARTIAL TRICYCLE SYSTEMS

In 1960, Trevor Evans gave a best possible embedding of a partial lati n square of order n in a latin square of order t, for any t greater th an or equal to 2n. A latin square of order n is equivalent to a 3-cycl e system of K-n,K-n,K-n, the complete tripartite graph. Here we consid er a small embedding of partial 3k-cycle systems of K-n,K-n,K-n of a c ertain type which generalizes Evans' Theorem, and discuss how this rel ates to the embedding of patterned holes, another recent generalizatio n of Evans' Theorem.