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Quarter-regular biembeddings of Latin squares. (English) Zbl 1228.05085

Summary: We apply a recursive construction for biembeddings of Latin squares to produce a new infinite family of biembeddings of cyclic Latin squares of even side having a high degree of symmetry. Reapplication of the construction yields two further classes of biembeddings.

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
Full Text: DOI

References:

[1] Archdeacon, D. S., Topological graph theory: a survey, Congr. Numer., 115, 5-54 (1996) · Zbl 0897.05026
[2] Grannell, M. J.; Griggs, T. S., Designs and topology, (Surveys in Combinatorics 2007’. Surveys in Combinatorics 2007’, London Math. Soc. Lecture Note Ser., vol. 346 (2007), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 121-174 · Zbl 1127.05013
[3] Grannell, M. J.; Griggs, T. S.; Knor, M., Biembeddings of Latin squares and Hamiltonian decompositions, Glasgow Math. J., 46, 443-457 (2004) · Zbl 1062.05030
[4] Grannell, M. J.; Griggs, T. S.; Knor, M.; Širáň, J., Triangulations of orientable surfaces by complete tripartite graphs, Discrete Math., 306, 600-606 (2006) · Zbl 1099.05025
[5] Stahl, S.; White, A. T., Genus embeddings for some complete tripartite graphs, Discrete Math., 14, 279-296 (1976) · Zbl 0322.05105
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