论文信息 - On Biembeddings of Latin Squares

On Biembeddings of Latin Squares

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 k 2 (k 6 2). In turn, these biembeddings enable us to increase the best known lower bound for the number of face 2-colourable triangular embeddings of Kn,n,n for an infinite class of values of n.

Mike J. Grannell | Terry S. Griggs | Martin Knor

[1] Mike J. Grannell,et al. Triangulations of orientable surfaces by complete tripartite graphs , 2006, Discret. Math..

[2] G. Ringel. Map Color Theorem , 1974 .

[3] Mike J. Grannell,et al. Recursive constructions for triangulations , 2002, J. Graph Theory.

[4] Mike J. Grannell,et al. A lower bound for the number of triangular embeddings of some complete graphs and complete regular tripartite graphs , 2008, J. Comb. Theory, Ser. B.

[5] Mike J. Grannell,et al. BIEMBEDDINGS OF LATIN SQUARES AND HAMILTONIAN DECOMPOSITIONS , 2004, Glasgow Mathematical Journal.

[6] Jonathan L. Gross,et al. Topological Graph Theory , 1987, Handbook of Graph Theory.

[7] Mike J. Grannell,et al. Biembeddings of Latin squares of side 8 , 2007 .

[8] C. Colbourn,et al. The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[9] Mike J. Grannell,et al. A constraint on the biembedding of Latin squares , 2009, Eur. J. Comb..