Minimum embedding of a KS ( u , λ ) into a KS ( u + w , μ )

Let H be a subgraph of a graph G. An H-design (U, C) of order u and index λ is embedded into a G-design (V , B) of order v and index μ if λ ≤ μ, U ⊆ V and there is an injective mapping f : C → B such that B is a subgraph of f (B) for every B ∈ C. The mapping f is called the embedding of (U, C) into (V , B). In this paper, we study the minimum embedding of a kite system of order u and index λ (denoted by KS(u, λ)) into a kite system of order u + w and index μ. © 2011 Elsevier B.V. All rights reserved.