Geodesic
On biembeddings of Latin squares
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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A known construction for face 2-colourable triangular embeddings of complete regular tripartite graphs is re-examined from the viewpoint of the underlying Latin squares. This facilitates biembeddings of a wide variety of Latin squares, including those formed from the Cayley tables of the elementary Abelian 2-groups $C_2^k$ ($k\ne 2$). In turn, these biembeddings enable us to increase the best known lower bound for the number of face 2-colourable triangular embeddings of $K_{n,n,n}$ for an infinite class of values of $n$.
DOI : 10.37236/195
Classification : 05B15, 05C10
Mots-clés : triangular embeddings, tripartite graphs, Latin squares, Cayley tables 
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     author = {M. J. Grannell and T. S. Griggs and M. Knor},
     title = {On biembeddings of {Latin} squares},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/195},
     zbl = {1186.05035},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/195/}
}
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M. J. Grannell; T. S. Griggs; M. Knor. On biembeddings of Latin squares. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/195

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