TBSs in some minimum coverings

Let (X,B) be a (λKn,G)-covering with excess E and a blocking set T. Let Γ1, Γ2, …, Γs be all connected components of E with at least two vertices (note that s=0 if E=0̸). The blocking set T is called tight if further V(Γi)∩T≠0̸ and V(Γi)∩(X∖T)≠0̸ 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=K3 and G=K3+e.