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A simple construction of disjoint and almost disjoint Steiner triple systems

โœ Scribed by Charles C Lindner

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
309 KB
Volume
17
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES

Steiner triple systems with two disjoint
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## 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}\choose 2}-{u\choose 2}- {w\choos

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โœ Charles J. Colbourn; Monica A. Oravas; Rolf S. Rees ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 225 KB ๐Ÿ‘ 1 views

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 ร€ 2z, the elementary necessary conditions are shown to be sufยฎcient for all values o

On the maximum number of disjoint Steine
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โœ Luc Teirlinck ๐Ÿ“‚ Article ๐Ÿ“… 1973 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 184 KB

Let D(u) be the maximum number of pairwk disjoint Steiner triple sysiems of order v. We prove that D(3v:r 2 2v + D(v) for every u = 1 oi 3 (mod 6), u 2 3. As a corollary, we have D(3n) -3n-2 for every n 2 1.