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Bi-Embeddings of Steiner Triple Systems of Order 15

✍ Scribed by G. K. Bennett; M. J. Grannell; T. S. Griggs

Book ID: 105745131
Publisher: Springer Japan
Year: 2001
Tongue: English
Weight: 71 KB
Volume: 17
Category: Article
ISSN: 0911-0119
DOI: 10.1007/pl00007240

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📜 SIMILAR VOLUMES

Embeddings of Steiner triple systems

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If X is a set whose elements are called points and A is a collectioxr of subsets of X (called lines) such that: (i) any two distinct points of X are contained in exactly one line, (ii) every line contains at least two points, we say that the pair (X, A) is a linear space. A Steiner triple system i

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A Steiner triple system of order n (STS(n)) is said to be embeddable in an orientable surface if there is an orientable embedding of the complete graph Kn whose faces can be properly 2-colored (say, black and white) in such a way that all black faces are triangles and these are precisely the blocks

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There are 80 non-isomorphic Steiner triple systems of order 15. A standard listing of these is given in Mathon et al. (1983, Ars Combin., 15, 3-110). We prove that systems #1 and #2 have no bi-embedding together in an orientable surface. This is the first known example of a pair of Steiner triple sy

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## Abstract In this paper, we present a conjecture that is a common generalization of the Doyen–Wilson Theorem and Lindner and Rosa's intersection theorem for Steiner triple systems. Given __u__, __v__ ≡ 1,3 (mod 6), __u__ < __v__ < 2__u__ + 1, we ask for the minimum __r__ such that there exists a

Cyclic bi-embeddings of Steiner triple s

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

✍ G. K. Bennett; M. J. Grannell; T. S. Griggs 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 196 KB 👁 1 views

## Abstract A cyclic face 2‐colourable triangulation of the complete graph __K__~__n__~ 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 eac