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Cyclic bi-embeddings of Steiner triple systems on 12s+7 points

Bennett, G.K.; Grannell, M.J. and Griggs, T.S. (2002). Cyclic bi-embeddings of Steiner triple systems on 12s+7 points. Journal of Combinatorial Designs, 10(2) pp. 92–110.

URL: http://www3.interscience.wiley.com/cgi-bin/abstrac...
DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1002/jcd.10001
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Abstract

A cyclic face 2-colourable triangulation of the complete graph Kn in an orientable surface exists for n 7 (mod 12). Such a triangulation corresponds to a cyclic bi-embedding of a pair of Steiner triple systems of order n, the triples being defined by the faces in each of the two colour classes. We investigate in the general case the production of such bi-embeddings from solutions to Heffter's first difference problem and appropriately labelled current graphs. For n = 19 and n = 31 we give a complete explanation for those pairs of Steiner triple systems which do not admit a cyclic bi-embedding and we show how all non-isomorphic solutions may be identified. For n = 43 we describe the structures of all possible current graphs and give a more detailed analysis in the case of the Heawood graph. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 92-110, 2002

Item Type: Journal Article
ISSN: 1063-8539
Keywords: Steiner triple system; Heffter's difference problem; topological embeddings of complete graphs
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2895
Depositing User: Terry Griggs
Date Deposited: 20 Jun 2006
Last Modified: 02 Dec 2010 19:48
URI: http://oro.open.ac.uk/id/eprint/2895
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