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Graphs and Combinatorics

, Volume 17, Issue 2, pp 193–197 | Cite as

Bi-Embeddings of Steiner Triple Systems of Order 15

  • G. K. Bennett
  • M. J. Grannell
  • T. S. Griggs

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 K15 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.

Key words. Topological embedding Triangulation of Kn Steiner triple system Non-isomorphic 
AMS classifications: 05B07 05C10 

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Copyright information

© Springer-Verlag Tokyo 2001

Authors and Affiliations

  • G. K. Bennett
    • 1
  • M. J. Grannell
    • 1
  • T. S. Griggs
    • 1
  1. 1.Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK. e-mail: m.j.grannell@open.ac.ukGB

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