Quarter-regular biembeddings of Latin squares
نویسندگان
چکیده
منابع مشابه
Quarter-regular biembeddings of Latin squares
In this talk I will review the concept of the biembedding of two latin squares. Of particular interest will be the regular biemedding of two isomorphic copies of the latin square corresponding to the cyclic group of order n, denoted Cn. Grannell and Griggs have shown that, for all n, a regular biembedding exists, and in addition, that the automorphism group of the regular biembedding has order ...
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For each positive integer n ≥ 2, there is a well-known regular orientable Hamiltonian embedding of Kn,n, and this generates a regular face 2-colourable triangular embedding of Kn,n,n. In the case n ≡ 0 (mod 8), and only in this case, there is a second regular orientable Hamiltonian embedding of Kn,n. The current paper presents an analysis of the face 2-colourable triangular embedding of Kn,n,n ...
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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 Ck 2 (k 6= 2). In turn, these biembeddings enable us to increase the best known ...
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An existing construction for face 2-colourable triangular embeddings of complete regular tripartite graphs is extended and then re-examined from the viewpoint of the underlying Latin squares. We prove that this generalization gives embeddings which are not isomorphic to any of those produced by the original construction.
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We investigate a voltage construction for face 2-colourable triangulations by Kn,n,n from the viewpoint of the underlying Latin squares. We prove that if the vertices are relabelled so that one of the Latin squares is exactly the Cayley table Cn of the group Zn, then the other square can be obtained from Cn by a cyclic permutation of row, column or entry identifiers, and we identify these cycli...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.08.020