Steiner triple systems with two disjoint subsystems
Contribuinte(s) |
C J Colbourn J D Dinitz PRJ Ostergard A Rosa |
---|---|
Data(s) |
01/01/2006
|
Resumo |
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. |
Identificador | |
Idioma(s) |
eng |
Publicador |
John Wiley & Sons Inc |
Palavras-Chave | #Steiner Triple System #Incomplete Steiner Triple System #Group Divisible Design #Mathematics #C1 #230101 Mathematical Logic, Set Theory, Lattices And Combinatorics #780101 Mathematical sciences |
Tipo |
Journal Article |