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Surface embeddings of Steiner triple systems

✍ Scribed by M. J. Grannell; T. S. Griggs; Jozef S˘irán˘

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 421 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:5<325::aid-jcd2>3.0.co;2-h

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✦ Synopsis

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 of the STS(n). If, in addition, all white faces are triangular, then the collection of all white triangles forms another STS(n); the pair of such STS(n)s is then said to have an (orientable) bi-embedding. We study several questions related to embeddings and bi-embeddings of STSs.

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