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Triangulations of orientable surfaces by complete tripartite graphs
, 2005
"... Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e n ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number, then the n ..."
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Cited by 7 (7 self)
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Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e n ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number
Nonorientable biembeddings . . .
 DISCRETE MATHEMATICS
, 2004
"... Constructions due to Ringel show that there exists a nonorientable face 2colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n ≡ 3 (mod 6) with n ≥ 9. We prove the corresponding existence th ..."
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Constructions due to Ringel show that there exists a nonorientable face 2colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n ≡ 3 (mod 6) with n ≥ 9. We prove the corresponding existence
A constraint on the biembedding of Latin squares
"... This is a preprint of an article accepted for publication in the European Journal of Combinatorics c©2008 (copyright owner as specified in the journal). We give a necessary condition for the biembedding of two Latin squares in an orientable surface. As a consequence, it is shown that for n ≥ 2, the ..."
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Cited by 3 (3 self)
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This is a preprint of an article accepted for publication in the European Journal of Combinatorics c©2008 (copyright owner as specified in the journal). We give a necessary condition for the biembedding of two Latin squares in an orientable surface. As a consequence, it is shown that for n ≥ 2
A construction for biembeddings of Latin squares
"... An existing construction for face 2colourable triangular embeddings of complete regular tripartite graphs is extended and then reexamined 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 ..."
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Cited by 4 (3 self)
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An existing construction for face 2colourable triangular embeddings of complete regular tripartite graphs is extended and then reexamined from the viewpoint of the underlying Latin squares. We prove that this generalization gives embeddings which are not isomorphic to any of those produced
Biembeddings of symmetric configurations and 3homogeneous Latin trades
"... This is a preprint of an article accepted for publication in Commentationes Mathematicae Universitatis Carolinae c©2008 (copyright owner as specified in the journal). Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the to ..."
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Cited by 1 (0 self)
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This is a preprint of an article accepted for publication in Commentationes Mathematicae Universitatis Carolinae c©2008 (copyright owner as specified in the journal). Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples
Biembeddings of the projective space PG(3, 2)
 JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 86, 2000, P321329
, 2000
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Biembeddings of Latin squares obtained from a voltage construction
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 51 (2011), PAGES 259–270
, 2011
"... We investigate a voltage construction for face 2colourable 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 ..."
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We investigate a voltage construction for face 2colourable 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
Comment.Math.Univ.Carolin. 49,3 (2008)411–420 411 Biembeddings of symmetric configurations and 3homogeneous Latin trades
"... Abstract. Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3homogeneous Latin trades. ..."
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Abstract. Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3homogeneous Latin trades.
Results 1  10
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12