Biembedding Abelian groups with mates having transversals

Grannell, M. J. and Knor, M. (2012). Biembedding Abelian groups with mates having transversals. Journal of Combinatorial Designs, 20(2) pp. 81–88.

DOI: https://doi.org/10.1002/jcd.20299

Abstract

A certain recursive construction for biembeddings of Latin squares has played a substantial role in generating large numbers of nonisomorphic triangular embeddings of complete graphs. In this paper we prove that, except for the groups $C_2, C_2^2$ and $C_4$, each Latin square formed from the Cayley table of an Abelian group appears in a biembedding in which the second Latin square has a transversal. Such biembeddings may then be freely used as ingredients in the recursive construction.

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