A constraint on the biembedding of Latin squares
Two Latin squares of order \(n\) are bi-embeddable in a surface, necessarily orientable, if there is a face 2-colorable triangular embedding of the complete tripartite graph \(K_{n,n,n}\) in which the face sets forming the two color classes give copies of the two squares. The authors provide a necessary condition for such bi-embeddings which enables them to show that for \(n\geq 2\) there is no bi-embedding of two Latin squares both lying in the same main class as the square obtained from the Cayley table of the Abelian 2-group \(C^n_2\), thereby giving the first known infinite class of pairs of Latin squares that admit no bi-embeddings.
scientific article; zbMATH DE number 5523088