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BIEMBEDDINGS OF LATIN SQUARES AND HAMILTONIAN DECOMPOSITIONS

Published online by Cambridge University Press:  11 October 2004

M. J. GRANNELL ,
T. S. GRIGGS  and
M. KNOR
M. J. GRANNELL
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom e-mail: m.j.grannell@open.ac.uk, t.s.griggs@open.ac.uk
T. S. GRIGGS
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom e-mail: m.j.grannell@open.ac.uk, t.s.griggs@open.ac.uk
M. KNOR
Affiliation:
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia e-mail: knor@vox.svf.stuba.sk
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Abstract

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Face 2-colourable triangulations of complete tripartite graphs $K_{n,n,n}$ correspond to biembeddings of Latin squares. Up to isomorphism, we give all such embeddings for $n=3,4,5$ and 6, and we summarize the corresponding results for $n=7$. Closely related to these are Hamiltonian decompositions of complete bipartite directed graphs $K^*_{n,n}$, and we also give computational results for these in the cases $n=3,4,5$ and 6.

Keywords

05B1505C10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 3 , September 2004 , pp. 443 - 457
Copyright
© 2004 Glasgow Mathematical Journal Trust