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A conjecture on small embeddings of partial Steiner triple systems

✍ Scribed by Darryn Bryant

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 106 KB
Volume: 10
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10017

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✦ Synopsis

Abstract

A well‐known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order υ for all υ ≡ 1 or 3, (mod 6), υ ≥ 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order υ <2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 313–321, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10017

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