A conjecture on small embeddings of partial Steiner triple systems

Bryant, D (2002) A conjecture on small embeddings of partial Steiner triple systems. Journal of Combinatorial Designs, 10 5: 313-321.


Author(s) Bryant, D
Title A conjecture on small embeddings of partial Steiner triple systems
Journal name Journal of Combinatorial Designs
Publication date 2002
Sub-type Article
Volume number 10
Issue number 5
ISBN 1063-8539
ISSN 1063-8539
Start page 313
End page 321
Total pages 9
Editor(s) C. Colbourn
Place of publication United States
Publisher John Wiley & Sons, Inc.
Collection year 2002
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
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 v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.
Keyword(s) Mathematics
Embeddings
Partial Triple Systems
Steiner Triple Systems
 
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