THIRD-REGULAR BI-EMBEDDINGS OF LATIN SQUARES

摘要

Abstract. For each positive integer n ≥ 2, there is awell-known regular orientablenHamiltonian embedding of Kn,n, and this generates a regular face 2-colourablentriangular embedding of Kn,n,n.Inthecase n ≡ 0 (mod 8), and only in this case, therenis a second regular orientable Hamiltonian embedding of Kn,n. This paper presentsnan analysis of the face 2-colourable triangular embedding of Kn,n,n that results fromnthis. The corresponding Latin squares of side n are determined, together with the fullnautomorphism group of the embedding.