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MAXIMUM GENUS EMBEDDINGS OF LATIN SQUARES

Part of: Graph theory Designs and configurations

Published online by Cambridge University Press:  30 October 2017

TERRY S. GRIGGS ,
CONSTANTINOS PSOMAS  and
JOZEF ŠIRÁŇ
TERRY S. GRIGGS
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom e-mail: t.s.griggs@open.ac.uk
CONSTANTINOS PSOMAS
Affiliation:
Department of Electrical and Computer Engineering, University of Cyprus, Nicosia 1678, Cyprus e-mail: psomas@ucy.ac.cy
JOZEF ŠIRÁŇ
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom e-mail: j.siran@open.ac.uk
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Abstract

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It is proved that every non-trivial Latin square has an upper embedding in a non-orientable surface and every Latin square of odd order has an upper embedding in an orientable surface. In the latter case, detailed results about the possible automorphisms and their actions are also obtained.

MSC classification

Primary: 05B15: Orthogonal arrays, Latin squares, Room squares
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 495 - 504
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

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