论文信息 - Biembedding Abelian groups with mates having transversals

Biembedding Abelian groups with mates having transversals

A certain recursive construction for biembeddings of Latin squares has played a substantial role in generating large numbers of nonisomorphic triangular embeddings of complete graphs. In this paper we prove that, except for the groups $C_2, C_2^2$ and $C_4$, each Latin square formed from the Cayley table of an Abelian group appears in a biembedding in which the second Latin square has a transversal. Such biembeddings may then be freely used as ingredients in the recursive construction.

Mike J. Grannell | M. Knor

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

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

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

[4] Mike J. Grannell,et al. On Biembeddings of Latin Squares , 2009, Electron. J. Comb..

[5] Mike J. Grannell,et al. Biembeddings of Abelian groups , 2009 .

[6] 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.