Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T23:01:55.969Z Has data issue: false hasContentIssue false
  • English
  • Français

THIRD-REGULAR BI-EMBEDDINGS OF LATIN SQUARES

Published online by Cambridge University Press:  25 August 2010

D. M. DONOVAN ,
M. J. GRANNELL  and
T. S. GRIGGS
D. M. DONOVAN
Affiliation:
Centre for Discrete Mathematics and Computing, University of Queensland, St Lucia 4072, Australia e-mail: [email protected]
M. J. GRANNELL
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK e-mail: [email protected]
T. S. GRIGGS
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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. This paper presents an analysis of the face 2-colourable triangular embedding of Kn, n, n that results from this. The corresponding Latin squares of side n are determined, together with the full automorphism group of the embedding.

Keywords

05B1505C10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 497 - 503
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Archdeacon, D., Topological graph theory – A survey, Congr. Numer. 115 (1996) 5–54.Google Scholar
2.Biggs, N. L. and White, A. T., Permutation groups and combinatorial structures (Cambridge University Press, Cambridge, UK, 1979).CrossRefGoogle Scholar
3.Donovan, D. M., Drápal, A., Grannell, M. J., Griggs, T. S. and Lefevre, J. G., Quarter-regular biembeddings of Latin squares, Discrete Math. 310 (2010) 692–699.CrossRefGoogle Scholar
4.Grannell, M. J., Griggs, T. S. and Knor, M., Regular Hamiltonian embeddings of the complete bipartite graph Kn,n in an orientable surface, Congr. Numer. 163 (2003) 197–205.Google Scholar
5.Grannell, M. J., Griggs, T. S. and Knor, M., Biembeddings of Latin squares and Hamiltonian decompositions, Glasgow Math. J. 46 (2004) 443–457.CrossRefGoogle Scholar
6.Grannell, M. J., Griggs, T. S., Knor, M. and Širáň, J., Triangulations of orientable surfaces by complete tripartite graphs, Discrete Math. 306 (2006) 600–606.CrossRefGoogle Scholar
7.Gross, J. L. and Tucker, T. W., Topological Graph Theory (John Wiley, New York, 1987).Google Scholar
8.Stahl, S. and White, A. T., Genus embeddings for some complete tripartite graphs, Discrete Math. 14 (1976) 279–296.CrossRefGoogle Scholar
9.White, A. T., Symmetrical maps, Congr. Numer. 45 (1984) 257–266.Google Scholar