Tight blocking sets in some maximum packings of [formula omitted

Abstract

Let ( X , B ) be a ( λ K n , G ) -packing with edge-leave L and a blocking set T. Let Γ 1 , Γ 2 , … , Γ s be all connected components of L with at least two vertices (note that s = 0 if L = ∅ ). The blocking set T is called tight if further V ( Γ i ) ∩ T ≠ ∅ and V ( Γ i ) ∩ ( X ⧹ T ) ≠ ∅ for 1 ⩽ i ⩽ s . In this paper we give a complete solution for the existence of a maximum ( λ K n , G ) -packing admitting a blocking set (BS), or a tight blocking set (TBS) for any λ , and G = K 3 , kite.