Let (X, B) be a (λ K_n, G)-packing with edge-leave L and a blocking set T. Let Γ_1, Γ_2, ..., Γ_s be all connected components of L with at least two vertices (note that s = 0 if L = ∅). The blocking set T is called tight if further V (Γ_i) ∩ T ≠ ∅ and V (Γ_i) ∩ (X {minus 45 degree rule} T) ≠ ∅ for 1 ≤ i ≤ s. In this paper we give a complete solution for the existence of a maximum (λ K_n, G)-packing admitting a blocking set (BS), or a tight blocking set (TBS) for any λ, and G = K_3, kite.
Tight blocking sets in some maximum packings of lambda K-n
LO FARO, Giovanni;TRIPODI, Antoinette
2008-01-01
Abstract
Let (X, B) be a (λ K_n, G)-packing with edge-leave L and a blocking set T. Let Γ_1, Γ_2, ..., Γ_s be all connected components of L with at least two vertices (note that s = 0 if L = ∅). The blocking set T is called tight if further V (Γ_i) ∩ T ≠ ∅ and V (Γ_i) ∩ (X {minus 45 degree rule} T) ≠ ∅ for 1 ≤ i ≤ s. In this paper we give a complete solution for the existence of a maximum (λ K_n, G)-packing admitting a blocking set (BS), or a tight blocking set (TBS) for any λ, and G = K_3, kite.File in questo prodotto:
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