Steiner triple systems with disjoint or intersecting subsystems

✍ Scribed by Charles J. Colbourn; Monica A. Oravas; Rolf S. Rees

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 225 KB
• Volume: 8
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(2000)8:1<58::aid-jcd8>3.0.co;2-2

✦ Synopsis

The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z 0) and intersecting (z 1) cases. When w ! u and v 2w u À 2z, the elementary necessary conditions are shown to be suf®cient for all values of z. Then for z P f0Y 1g and v ``near'' the minimum of 2w u À 2 z, the conditions are again shown to be suf®cient. Consequences for larger orders are also discussed, in particular the proof that when one hole is at least three times as large as the other, the conditions are again suf®cient.