Steiner triple systems with two disjoint subsystems

Darryn Bryant, Daniel Horsley

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


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) a? 0 (mod3), and v a?Y 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
Original languageEnglish
Pages (from-to)14 - 24
Number of pages11
JournalJournal of Combinatorial Designs
Issue number1
Publication statusPublished - 2006
Externally publishedYes

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