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

VL - 309

SP - 400

EP - 411

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -