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W4213064655 abstract "A ( K 4 − 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 ( K 4 − e ) -design of order v + w ? We solve the problem for 7 of the 10 congruence classes modulo 30." @default.
W4213064655 created "2022-02-24" @default.
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W4213064655 date "2009-01-01" @default.
W4213064655 modified "2023-09-27" @default.
W4213064655 title "Minimum embedding of Steiner triple systems into <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-designs II" @default.
W4213064655 cites W2032063366 @default.
W4213064655 doi "https://doi.org/10.1016/j.disc.2007.12.026" @default.
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