On tight blocking set in 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=∅). 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=K3 and G=K3+e.