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Bi-embeddings of Steiner triple systems of order 15

Bennett, G. K.; Grannell, M. J. and Griggs, T. S. (2001). Bi-embeddings of Steiner triple systems of order 15. Graphs and Combinatorics, 17(2) pp. 193–197.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/PL00007240
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Abstract

It was shown by Gerhard Ringel that one of the three non-isomorphic Steiner triple systems of order 15 having an automorphism of order 5 may be bi-embedded as the faces of a face 2-colourable triangular embedding of $K_{15}$ in a suitable orientable surface. Ringel's bi-embedding was obtained from an appropriate current graph. In a recent paper, the present authors showed that a second STS(15) of this type may also be bi-embedded. In the present paper we show that this second bi-embedding may also be obtained from a current graph. Furthermore, we exhibit a third current graph which yields a bi-embedding of the third STS(15) of this type.

Item Type: Journal Article
ISSN: 1435-5914
Keywords: topological embedding; triangulation of Kn; Steiner triple system; non-isomorphic
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22782
Depositing User: Mike Grannell
Date Deposited: 18 Aug 2010 13:29
Last Modified: 02 Dec 2010 21:02
URI: http://oro.open.ac.uk/id/eprint/22782
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