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 ) are non empty sets for 1 ≤ i ≤ s. In this paper, we give a complete solution for the existence of a minimum (λK_n, 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.
TBSs in some 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 ) are non empty sets for 1 ≤ i ≤ s. In this paper, we give a complete solution for the existence of a minimum (λK_n, 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.File in questo prodotto:
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