Let H be a subgraph of G. An H-design (X, C) of order v − w, 0 ≤ w ≤ v, and index μ is embedded into a G-design (V, B) of order v and index λ, if μ ≤λ X ⊆ V and there is an injective mapping f : C ! B such that B is subgraph of f (B) for every B ∈ C. For every pair of positive integers v≥4, we determine the minimum value of w such that there exists a balanced incomplete block design of order v, index λ≥ 2 and block-size 4 which embeds a K3-design of order v − w, 0 ≤w ≤ v, and index μ = 1.
On the existence of an S_l(2,4,v) which embeds an S(2,3,v-w) of maximum order for lambda≥2
MILICI, Salvatore;
2010-01-01
Abstract
Let H be a subgraph of G. An H-design (X, C) of order v − w, 0 ≤ w ≤ v, and index μ is embedded into a G-design (V, B) of order v and index λ, if μ ≤λ X ⊆ V and there is an injective mapping f : C ! B such that B is subgraph of f (B) for every B ∈ C. For every pair of positive integers v≥4, we determine the minimum value of w such that there exists a balanced incomplete block design of order v, index λ≥ 2 and block-size 4 which embeds a K3-design of order v − w, 0 ≤w ≤ v, and index μ = 1.File in questo prodotto:
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