Article
On the Biembeddability of Certain Steiner Triple Systems of Order 15
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, .ukf1
European Journal of Combinatorics (Impact Factor: 0.66). 01/2002; DOI: 10.1006/eujc.2002.0559 Source: OAI

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Nephrologie & Therapeutique  NEPHROL THER. 01/2011; 7(5):310310.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we describe the generation of all nonorientable triangular embeddings of the complete graphs K12 and K13. (The 59 nonisomorphic orientable triangular embeddings of K12 were found in 1996 by Altshuler, Bokowski, and Schuchert, and K13 has no orientable triangular embeddings.) There are 182,200 nonisomorphic nonorientable triangular embeddings for K12, and 243,088,286 for K13. Triangular embeddings of complete graphs are also known as neighborly maps and are a type of twofold triple system. We also use methods of Wilson to provide an upper bound on the number of simple twofold triple systems of order n, and thereby on the number of triangular embeddings of Kn. We mention an application of our results to flexibility of embedded graphs. © 2005 Wiley Periodicals, Inc. J Combin DesignsJournal of Combinatorial Designs 08/2005; 13(5):336  344. · 0.69 Impact Factor 
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