Steiner triple systems with two disjoint subsystems

Bryant, D and Horsley, D (2006) Steiner triple systems with two disjoint subsystems. Journal of Combinatorial Designs, 14 1: 14-24. doi:10.1002/jcd.20071


Author Bryant, D
Horsley, D
Title Steiner triple systems with two disjoint subsystems
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1063-8539
Publication date 2006-01-01
Sub-type Article (original research)
DOI 10.1002/jcd.20071
Volume 14
Issue 1
Start page 14
End page 24
Total pages 11
Editor C J Colbourn
J D Dinitz
PRJ Ostergard
A Rosa
Place of publication Hoboken
Publisher John Wiley & Sons Inc
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.
Keyword Steiner Triple System
Incomplete Steiner Triple System
Group Divisible Design
Mathematics
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 19:15:48 EST