Let (X,B) be a (λK_n, G)-covering with excess E and a blocking set T. Let Γ_1,Γ_2, ..., Γ_s be all connected components of E with at least two vertices (note that s = 0 if E = ∅). The blocking set T is called tight if further V (Γi) ∩ T = ∅ and V (Γi) ∩ (X \ T) = ∅ for 1 ≤ i ≤ s. In this paper we give a complete solution for the existence of a minimum (λKn, G)-covering admitting a blocking set (BS), or a tight blocking set (TBS) for any λ and when G = K_3 and G = K_3+e
On tight blocking set in minimum coverings
LO FARO, Giovanni;TRIPODI, Antoinette;
2013-01-01
Abstract
Let (X,B) be a (λK_n, G)-covering with excess E and a blocking set T. Let Γ_1,Γ_2, ..., Γ_s be all connected components of E with at least two vertices (note that s = 0 if E = ∅). The blocking set T is called tight if further V (Γi) ∩ T = ∅ and V (Γi) ∩ (X \ T) = ∅ for 1 ≤ i ≤ s. In this paper we give a complete solution for the existence of a minimum (λKn, G)-covering admitting a blocking set (BS), or a tight blocking set (TBS) for any λ and when G = K_3 and G = K_3+eFile in questo prodotto:
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