Tight blocking sets in some maximum packings of λKnλKn

Let (X,B)(X,B) be a (λKn,G)(λKn,G)-packing with edge-leave L and a blocking set T  . Let Γ1,Γ2,…,ΓsΓ1,Γ2,…,Γs be all connected components of L   with at least two vertices (note that s=0s=0 if L=∅L=∅). The blocking set T   is called tight if further V(Γi)∩T≠∅V(Γi)∩T≠∅ and V(Γi)∩(X⧹T)≠∅V(Γi)∩(X⧹T)≠∅ for 1⩽i⩽s1⩽i⩽s. In this paper we give a complete solution for the existence of a maximum (λKn,G)(λKn,G)-packing admitting a blocking set (BS), or a tight blocking set (TBS) for any λλ, and G=K3G=K3, kite.