Biembeddings of 2-Rotational Steiner Triple Systems
نویسندگان
چکیده
It is shown that for v ≡ 1 or 3 (mod 6), every pair of Heffter difference sets modulo v gives rise to a biembedding of two 2-rotational Steiner triple systems of order 2v + 1 in a nonorientable surface. AMS classification: 05C10.
منابع مشابه
A census of the orientable biembeddings of Steiner triple systems of order 15
A complete census is given of the orientable biembeddings of Steiner triple systems of order 15. There are 80 Steiner triple systems of order 15 and these generate a total of 9 530 orientable biembeddings.
متن کاملOrientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs
We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n + 1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our charact...
متن کاملNonorientable biembeddings of Steiner triple systems
It is shown that each possible pair of the 80 isomorphism classes of Steiner triple systems of order 15 may be realized as the colour classes of a face 2-colourable triangulation of the complete graph in a non-orientable surface. This supports the conjecture that every pair of STS(n)s, n ≥ 9, can be biembedded in a non-orientable surface. AMS classification: 05B07, 05C10.
متن کاملNon - Orientable Biembeddings of Steiner Triple Systems of Order 15
It is shown that each possible pair of the 80 isomorphism classes of Steiner triple systems of order 15 may be realized as the colour classes of a face 2-colourable triangulation of the complete graph in a non-orientable surface. This supports the conjecture that every pair of STS(n)s, n ≥ 9, can be biembedded in a non-orientable surface.
متن کاملFace Two-colourable Triangulations of K 13
Face two-colourable triangular embeddings of complete graphs Kn correspond to biembeddings of Steiner triple systems. Such embeddings exist only if n is congruent to 1 or 3 modulo 6. In this paper we present the number of these embeddings for n = 13.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015