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Some new perfect Steiner triple systems

✍ Scribed by M. J. Grannell; T. S. Griggs; J. P. Murphy

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 147 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:5<327::aid-jcd3>3.0.co;2-s

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✦ Synopsis

In a Steiner triple system STS(v) = (V, B), for each pair {a, b} ⊂ V, the cycle graph G a,b can be defined as follows. The vertices of G a,b are V \ {a, b, c} where {a, b, c} ∈ B. {x, y} is an edge if either {a, x, y} or {b, x, y} ∈ B. The Steiner triple system is said to be perfect if the cycle graph of every pair is a single (v-3)-cycle. Perfect STS(v) are known only for v = 7, 9, 25, and 33. We construct perfect STS(v) for v = 79, 139, 367, 811,

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