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: https://doi.org/10.1007/PL00007240

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.

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