TY - JOUR
T1 - Minimum embedding of Steiner triple systems into (K4 - e)-designs II
AU - Ling, Alan C H
AU - Colbourn, Charles
AU - Quattrocchi, Gaetano
N1 - Funding Information:
Most of the work was carried out when the second author visited University of Catania sponsored by INDAM-GNSAGA. The hospitality of the department is greatly appreciated. The research of the third author is sponsored by MIUR-Italy and CNR-GNSAGA.
PY - 2009/1/28
Y1 - 2009/1/28
N2 - A (K4 - e)-design of order v + w embeds a given Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of the original Steiner triple system. It has been established that w ≥ v / 3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when v = 15. Equality only holds when v ≡ 15, 27 (mod 30). One natural question is: What is the smallest order w such that some STS(v) can be embedded into a (K4 - e)-design of order v + w? We solve the problem for 7 of the 10 congruence classes modulo 30.
AB - A (K4 - e)-design of order v + w embeds a given Steiner triple system if there is a subset of v points on which the graphs of the design induce the blocks of the original Steiner triple system. It has been established that w ≥ v / 3, and that when equality is met, such a minimum embedding of an STS(v) exists, except when v = 15. Equality only holds when v ≡ 15, 27 (mod 30). One natural question is: What is the smallest order w such that some STS(v) can be embedded into a (K4 - e)-design of order v + w? We solve the problem for 7 of the 10 congruence classes modulo 30.
KW - Embedding
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U2 - 10.1016/j.disc.2007.12.026
DO - 10.1016/j.disc.2007.12.026
M3 - Article
AN - SCOPUS:56649109589
SN - 0012-365X
VL - 309
SP - 400
EP - 411
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 2
ER -